diff --git a/include/proto/connection.h b/include/proto/connection.h
index a2bcc97e6..e55ec8bef 100644
--- a/include/proto/connection.h
+++ b/include/proto/connection.h
@@ -315,25 +315,25 @@ static inline void __conn_xprt_stop_recv(struct connection *c)
 	c->flags &= ~CO_FL_XPRT_RD_ENA;
 }
 
-static inline void __cs_data_want_recv(struct conn_stream *cs)
+static inline void __cs_want_recv(struct conn_stream *cs)
 {
 	cs->flags |= CS_FL_DATA_RD_ENA;
 }
 
-static inline void __cs_data_stop_recv(struct conn_stream *cs)
+static inline void __cs_stop_recv(struct conn_stream *cs)
 {
 	cs->flags &= ~CS_FL_DATA_RD_ENA;
 }
 
-static inline void cs_data_want_recv(struct conn_stream *cs)
+static inline void cs_want_recv(struct conn_stream *cs)
 {
-	__cs_data_want_recv(cs);
+	__cs_want_recv(cs);
 	cs_update_mux_polling(cs);
 }
 
-static inline void cs_data_stop_recv(struct conn_stream *cs)
+static inline void cs_stop_recv(struct conn_stream *cs)
 {
-	__cs_data_stop_recv(cs);
+	__cs_stop_recv(cs);
 	cs_update_mux_polling(cs);
 }
 
@@ -366,36 +366,36 @@ static inline void __conn_xprt_stop_both(struct connection *c)
 	c->flags &= ~(CO_FL_XPRT_WR_ENA | CO_FL_XPRT_RD_ENA);
 }
 
-static inline void __cs_data_want_send(struct conn_stream *cs)
+static inline void __cs_want_send(struct conn_stream *cs)
 {
 	cs->flags |= CS_FL_DATA_WR_ENA;
 }
 
-static inline void __cs_data_stop_send(struct conn_stream *cs)
+static inline void __cs_stop_send(struct conn_stream *cs)
 {
 	cs->flags &= ~CS_FL_DATA_WR_ENA;
 }
 
-static inline void cs_data_stop_send(struct conn_stream *cs)
+static inline void cs_stop_send(struct conn_stream *cs)
 {
-	__cs_data_stop_send(cs);
+	__cs_stop_send(cs);
 	cs_update_mux_polling(cs);
 }
 
-static inline void cs_data_want_send(struct conn_stream *cs)
+static inline void cs_want_send(struct conn_stream *cs)
 {
-	__cs_data_want_send(cs);
+	__cs_want_send(cs);
 	cs_update_mux_polling(cs);
 }
 
-static inline void __cs_data_stop_both(struct conn_stream *cs)
+static inline void __cs_stop_both(struct conn_stream *cs)
 {
 	cs->flags &= ~(CS_FL_DATA_WR_ENA | CS_FL_DATA_RD_ENA);
 }
 
-static inline void cs_data_stop_both(struct conn_stream *cs)
+static inline void cs_stop_both(struct conn_stream *cs)
 {
-	__cs_data_stop_both(cs);
+	__cs_stop_both(cs);
 	cs_update_mux_polling(cs);
 }
 
@@ -537,6 +537,45 @@ static inline void conn_xprt_shutw_hard(struct connection *c)
 		c->xprt->shutw(c, 0);
 }
 
+/* shut read after draining possibly pending data */
+static inline void cs_shutr(struct conn_stream *cs)
+{
+	__cs_stop_recv(cs);
+
+	/* clean data-layer shutdown */
+	if (cs->conn->mux && cs->conn->mux->shutr)
+		cs->conn->mux->shutr(cs, 1);
+}
+
+/* shut read after disabling lingering */
+static inline void cs_shutr_hard(struct conn_stream *cs)
+{
+	__cs_stop_recv(cs);
+
+	/* clean data-layer shutdown */
+	if (cs->conn->mux && cs->conn->mux->shutr)
+		cs->conn->mux->shutr(cs, 0);
+}
+
+static inline void cs_shutw(struct conn_stream *cs)
+{
+	__cs_stop_send(cs);
+
+	/* clean data-layer shutdown */
+	if (cs->conn->mux && cs->conn->mux->shutw)
+		cs->conn->mux->shutw(cs, 1);
+}
+
+static inline void cs_shutw_hard(struct conn_stream *cs)
+{
+	__cs_stop_send(cs);
+
+	/* unclean data-layer shutdown */
+	if (cs->conn->mux && cs->conn->mux->shutw)
+		cs->conn->mux->shutw(cs, 0);
+}
+
+
 /* detect sock->data read0 transition */
 static inline int conn_xprt_read0_pending(struct connection *c)
 {
@@ -576,7 +615,6 @@ static inline void conn_init(struct connection *conn)
 {
 	conn->obj_type = OBJ_TYPE_CONN;
 	conn->flags = CO_FL_NONE;
-	conn->data = NULL;
 	conn->tmp_early_data = -1;
 	conn->mux = NULL;
 	conn->mux_ctx = NULL;
@@ -622,31 +660,43 @@ static inline struct connection *conn_new()
 	return conn;
 }
 
-/* Tries to allocate a new conn_stream and initialize its main fields. The
- * connection is returned on success, NULL on failure. The connection must
- * be released using pool_free2() or conn_free().
- */
-static inline struct conn_stream *cs_new(struct connection *conn)
-{
-	struct conn_stream *cs;
-
-	cs = pool_alloc2(pool2_connstream);
-	if (likely(cs != NULL))
-		cs_init(cs, conn);
-	return cs;
-}
-
 /* Releases a conn_stream previously allocated by cs_new() */
 static inline void cs_free(struct conn_stream *cs)
 {
 	pool_free2(pool2_connstream, cs);
 }
 
+/* Tries to allocate a new conn_stream and initialize its main fields. If
+ * <conn> is NULL, then a new connection is allocated on the fly, initialized,
+ * and assigned to cs->conn ; this connection will then have to be released
+ * using pool_free2() or conn_free(). The conn_stream is initialized and added
+ * to the mux's stream list on success, then returned. On failure, nothing is
+ * allocated and NULL is returned.
+ */
+static inline struct conn_stream *cs_new(struct connection *conn)
+{
+	struct conn_stream *cs;
+
+	cs = pool_alloc2(pool2_connstream);
+	if (!likely(cs))
+		return NULL;
+
+	if (!conn) {
+		conn = conn_new();
+		if (!likely(conn)) {
+			cs_free(cs);
+			return NULL;
+		}
+		conn_init(conn);
+	}
+
+	cs_init(cs, conn);
+	return cs;
+}
+
 /* Releases a connection previously allocated by conn_new() */
 static inline void conn_free(struct connection *conn)
 {
-	if (conn->mux && conn->mux->release)
-		conn->mux->release(conn);
 	pool_free2(pool2_connection, conn);
 }
 
@@ -700,11 +750,11 @@ static inline void conn_get_to_addr(struct connection *conn)
 	conn->flags |= CO_FL_ADDR_TO_SET;
 }
 
-/* Attaches a connection to an owner and assigns a data layer */
-static inline void conn_attach(struct connection *conn, void *owner, const struct data_cb *data)
+/* Attaches a conn_stream to a data layer and sets the relevant callbacks */
+static inline void cs_attach(struct conn_stream *cs, void *data, const struct data_cb *data_cb)
 {
-	conn->data = data;
-	conn->owner = owner;
+	cs->data_cb = data_cb;
+	cs->data = data;
 }
 
 /* Installs the connection's mux layer for upper context <ctx>.
@@ -789,11 +839,11 @@ static inline const char *conn_get_mux_name(const struct connection *conn)
 	return conn->mux->name;
 }
 
-static inline const char *conn_get_data_name(const struct connection *conn)
+static inline const char *cs_get_data_name(const struct conn_stream *cs)
 {
-	if (!conn->data)
+	if (!cs->data_cb)
 		return "NONE";
-	return conn->data->name;
+	return cs->data_cb->name;
 }
 
 /* registers pointer to transport layer <id> (XPRT_*) */
diff --git a/include/proto/stream.h b/include/proto/stream.h
index 3efb42bac..f0edc2ef4 100644
--- a/include/proto/stream.h
+++ b/include/proto/stream.h
@@ -36,7 +36,7 @@ extern struct list streams;
 extern struct data_cb sess_conn_cb;
 
 struct stream *stream_new(struct session *sess, enum obj_type *origin);
-int stream_create_from_conn(struct connection *conn);
+int stream_create_from_cs(struct conn_stream *cs);
 
 /* perform minimal intializations, report 0 in case of error, 1 if OK. */
 int init_stream();
diff --git a/include/proto/stream_interface.h b/include/proto/stream_interface.h
index c6578ef07..ee1fa124a 100644
--- a/include/proto/stream_interface.h
+++ b/include/proto/stream_interface.h
@@ -152,18 +152,14 @@ static inline enum obj_type *si_detach_endpoint(struct stream_interface *si)
  */
 static inline void si_release_endpoint(struct stream_interface *si)
 {
-	struct connection *conn;
+	struct conn_stream *cs;
 	struct appctx *appctx;
 
 	if (!si->end)
 		return;
 
-	if ((conn = objt_conn(si->end))) {
-		LIST_DEL(&conn->list);
-		conn_stop_tracking(conn);
-		conn_full_close(conn);
-		conn_free(conn);
-	}
+	if ((cs = objt_cs(si->end)))
+		cs_destroy(cs);
 	else if ((appctx = objt_appctx(si->end))) {
 		if (appctx->applet->release && si->state < SI_ST_DIS)
 			appctx->applet->release(appctx);
@@ -178,26 +174,27 @@ static inline void si_release_endpoint(struct stream_interface *si)
  * connection will also be added at the head of this list. This connection
  * remains assigned to the stream interface it is currently attached to.
  */
-static inline void si_idle_conn(struct stream_interface *si, struct list *pool)
+static inline void si_idle_cs(struct stream_interface *si, struct list *pool)
 {
-	struct connection *conn = __objt_conn(si->end);
+	struct conn_stream *cs = __objt_cs(si->end);
+	struct connection *conn = cs->conn;
 
 	if (pool)
 		LIST_ADD(pool, &conn->list);
 
-	conn_attach(conn, si, &si_idle_conn_cb);
-	conn_xprt_want_recv(conn);
+	cs_attach(cs, si, &si_idle_conn_cb);
+	cs_want_recv(cs);
 }
 
-/* Attach connection <conn> to the stream interface <si>. The stream interface
+/* Attach conn_stream <cs> to the stream interface <si>. The stream interface
  * is configured to work with a connection and the connection it configured
  * with a stream interface data layer.
  */
-static inline void si_attach_conn(struct stream_interface *si, struct connection *conn)
+static inline void si_attach_cs(struct stream_interface *si, struct conn_stream *cs)
 {
 	si->ops = &si_conn_ops;
-	si->end = &conn->obj_type;
-	conn_attach(conn, si, &si_conn_cb);
+	si->end = &cs->obj_type;
+	cs_attach(cs, si, &si_conn_cb);
 }
 
 /* Returns true if a connection is attached to the stream interface <si> and
@@ -205,7 +202,7 @@ static inline void si_attach_conn(struct stream_interface *si, struct connection
  */
 static inline int si_conn_ready(struct stream_interface *si)
 {
-	struct connection *conn = objt_conn(si->end);
+	struct connection *conn = cs_conn(objt_cs(si->end));
 
 	return conn && conn_ctrl_ready(conn) && conn_xprt_ready(conn);
 }
@@ -276,22 +273,22 @@ static inline void si_applet_stop_get(struct stream_interface *si)
 	si->flags &= ~SI_FL_WANT_GET;
 }
 
-/* Try to allocate a new connection and assign it to the interface. If
+/* Try to allocate a new conn_stream and assign it to the interface. If
  * an endpoint was previously allocated, it is released first. The newly
- * allocated connection is initialized, assigned to the stream interface,
+ * allocated conn_stream is initialized, assigned to the stream interface,
  * and returned.
  */
-static inline struct connection *si_alloc_conn(struct stream_interface *si)
+static inline struct conn_stream *si_alloc_cs(struct stream_interface *si, struct connection *conn)
 {
-	struct connection *conn;
+	struct conn_stream *cs;
 
 	si_release_endpoint(si);
 
-	conn = conn_new();
-	if (conn)
-		si_attach_conn(si, conn);
+	cs = cs_new(conn);
+	if (cs)
+		si_attach_cs(si, cs);
 
-	return conn;
+	return cs;
 }
 
 /* Release the interface's existing endpoint (connection or appctx) and
@@ -346,7 +343,8 @@ static inline void si_chk_snd(struct stream_interface *si)
 /* Calls chk_snd on the connection using the ctrl layer */
 static inline int si_connect(struct stream_interface *si)
 {
-	struct connection *conn = objt_conn(si->end);
+	struct conn_stream *cs = objt_cs(si->end);
+	struct connection *conn = cs_conn(cs);
 	int ret = SF_ERR_NONE;
 
 	if (unlikely(!conn || !conn->ctrl || !conn->ctrl->connect))
@@ -364,7 +362,7 @@ static inline int si_connect(struct stream_interface *si)
 		/* reuse the existing connection */
 		if (!channel_is_empty(si_oc(si))) {
 			/* we'll have to send a request there. */
-			conn_xprt_want_send(conn);
+			cs_want_send(cs);
 		}
 
 		/* the connection is established */
diff --git a/include/types/checks.h b/include/types/checks.h
index 3559f2d52..ac3e7b644 100644
--- a/include/types/checks.h
+++ b/include/types/checks.h
@@ -157,7 +157,7 @@ enum {
 
 struct check {
 	struct xprt_ops *xprt;			/* transport layer operations for health checks */
-	struct connection *conn;		/* connection state for health checks */
+	struct conn_stream *cs;			/* conn_stream state for health checks */
 	unsigned short port;			/* the port to use for the health checks */
 	struct buffer *bi, *bo;			/* input and output buffers to send/recv check */
 	struct task *task;			/* the task associated to the health check processing, NULL if disabled */
diff --git a/include/types/connection.h b/include/types/connection.h
index 66ec1b6b1..0d62efc99 100644
--- a/include/types/connection.h
+++ b/include/types/connection.h
@@ -288,9 +288,9 @@ struct mux_ops {
  * data movement. It may abort a connection by returning < 0.
  */
 struct data_cb {
-	void (*recv)(struct connection *conn);  /* data-layer recv callback */
-	void (*send)(struct connection *conn);  /* data-layer send callback */
-	int  (*wake)(struct connection *conn);  /* data-layer callback to report activity */
+	void (*recv)(struct conn_stream *cs);  /* data-layer recv callback */
+	void (*send)(struct conn_stream *cs);  /* data-layer send callback */
+	int  (*wake)(struct conn_stream *cs);  /* data-layer callback to report activity */
 	char name[8];                           /* data layer name, zero-terminated */
 };
 
@@ -347,10 +347,9 @@ struct connection {
 	const struct protocol *ctrl;  /* operations at the socket layer */
 	const struct xprt_ops *xprt;  /* operations at the transport layer */
 	const struct mux_ops  *mux;   /* mux layer opreations. Must be set before xprt->init() */
-	const struct data_cb  *data;  /* data layer callbacks. Must be set before xprt->init() */
 	void *xprt_ctx;               /* general purpose pointer, initialized to NULL */
 	void *mux_ctx;                /* mux-specific context, initialized to NULL */
-	void *owner;                  /* pointer to upper layer's entity (eg: session, stream interface) */
+	void *owner;                  /* pointer to the owner session for incoming connections, or NULL */
 	int xprt_st;                  /* transport layer state, initialized to zero */
 	int tmp_early_data;           /* 1st byte of early data, if any */
 	union conn_handle handle;     /* connection handle at the socket layer */
diff --git a/src/backend.c b/src/backend.c
index 4d44e5499..9dbbd9198 100644
--- a/src/backend.c
+++ b/src/backend.c
@@ -567,7 +567,7 @@ int assign_server(struct stream *s)
 
 	srv = NULL;
 	s->target = NULL;
-	conn = objt_conn(s->si[1].end);
+	conn = cs_conn(objt_cs(s->si[1].end));
 
 	if (conn &&
 	    (conn->flags & CO_FL_CONNECTED) &&
@@ -720,8 +720,7 @@ int assign_server(struct stream *s)
 		s->target = &s->be->obj_type;
 	}
 	else if ((s->be->options & PR_O_HTTP_PROXY) &&
-		 (conn = objt_conn(s->si[1].end)) &&
-		 is_addr(&conn->addr.to)) {
+		 conn && is_addr(&conn->addr.to)) {
 		/* in proxy mode, we need a valid destination address */
 		s->target = &s->be->obj_type;
 	}
@@ -769,7 +768,7 @@ int assign_server(struct stream *s)
 int assign_server_address(struct stream *s)
 {
 	struct connection *cli_conn = objt_conn(strm_orig(s));
-	struct connection *srv_conn = objt_conn(s->si[1].end);
+	struct connection *srv_conn = cs_conn(objt_cs(s->si[1].end));
 
 #ifdef DEBUG_FULL
 	fprintf(stderr,"assign_server_address : s=%p\n",s);
@@ -973,7 +972,7 @@ static void assign_tproxy_address(struct stream *s)
 	struct server *srv = objt_server(s->target);
 	struct conn_src *src;
 	struct connection *cli_conn;
-	struct connection *srv_conn = objt_conn(s->si[1].end);
+	struct connection *srv_conn = cs_conn(objt_cs(s->si[1].end));
 
 	if (srv && srv->conn_src.opts & CO_SRC_BIND)
 		src = &srv->conn_src;
@@ -1041,21 +1040,23 @@ int connect_server(struct stream *s)
 {
 	struct connection *cli_conn;
 	struct connection *srv_conn;
-	struct connection *old_conn;
+	struct conn_stream *srv_cs;
+	struct conn_stream *old_cs;
 	struct server *srv;
 	int reuse = 0;
 	int err;
 
 	srv = objt_server(s->target);
-	srv_conn = objt_conn(s->si[1].end);
+	srv_cs = objt_cs(s->si[1].end);
+	srv_conn = cs_conn(srv_cs);
 	if (srv_conn)
 		reuse = s->target == srv_conn->target;
 
 	if (srv && !reuse) {
-		old_conn = srv_conn;
-		if (old_conn) {
+		old_cs = srv_cs;
+		if (old_cs) {
 			srv_conn = NULL;
-			old_conn->owner = NULL;
+			srv_cs->data = NULL;
 			si_detach_endpoint(&s->si[1]);
 			/* note: if the connection was in a server's idle
 			 * queue, it doesn't get dequeued.
@@ -1101,23 +1102,25 @@ int connect_server(struct stream *s)
 			LIST_DEL(&srv_conn->list);
 			LIST_INIT(&srv_conn->list);
 
-			if (srv_conn->owner) {
-				si_detach_endpoint(srv_conn->owner);
-				if (old_conn && !(old_conn->flags & CO_FL_PRIVATE)) {
-					si_attach_conn(srv_conn->owner, old_conn);
-					si_idle_conn(srv_conn->owner, NULL);
+			/* XXX cognet: this assumes only 1 conn_stream per
+			 * connection, has to be revisited later
+			 */
+			srv_cs = srv_conn->mux_ctx;
+
+			if (srv_conn->mux == &mux_pt_ops && srv_cs->data) {
+				si_detach_endpoint(srv_cs->data);
+				if (old_cs && !(old_cs->conn->flags & CO_FL_PRIVATE)) {
+					si_attach_cs(srv_cs->data, old_cs);
+					si_idle_cs(srv_cs->data, NULL);
 				}
 			}
-			si_attach_conn(&s->si[1], srv_conn);
+			si_attach_cs(&s->si[1], srv_cs);
 			reuse = 1;
 		}
 
 		/* we may have to release our connection if we couldn't swap it */
-		if (old_conn && !old_conn->owner) {
-			LIST_DEL(&old_conn->list);
-			conn_full_close(old_conn);
-			conn_free(old_conn);
-		}
+		if (old_cs && !old_cs->data)
+			cs_destroy(old_cs);
 	}
 
 	if (reuse) {
@@ -1136,15 +1139,16 @@ int connect_server(struct stream *s)
 		}
 	}
 
-	if (!reuse)
-		srv_conn = si_alloc_conn(&s->si[1]);
-	else {
+	if (!reuse) {
+		srv_cs = si_alloc_cs(&s->si[1], NULL);
+		srv_conn = cs_conn(srv_cs);
+	} else {
 		/* reusing our connection, take it out of the idle list */
 		LIST_DEL(&srv_conn->list);
 		LIST_INIT(&srv_conn->list);
 	}
 
-	if (!srv_conn)
+	if (!srv_cs)
 		return SF_ERR_RESOURCE;
 
 	if (!(s->flags & SF_ADDR_SET)) {
@@ -1160,14 +1164,16 @@ int connect_server(struct stream *s)
 		/* set the correct protocol on the output stream interface */
 		if (srv) {
 			conn_prepare(srv_conn, protocol_by_family(srv_conn->addr.to.ss_family), srv->xprt);
-			conn_install_mux(srv_conn, &mux_pt_ops, srv_conn);
+			/* XXX: Pick the right mux, when we finally have one */
+			conn_install_mux(srv_conn, &mux_pt_ops, srv_cs);
 		}
 		else if (obj_type(s->target) == OBJ_TYPE_PROXY) {
 			/* proxies exclusively run on raw_sock right now */
 			conn_prepare(srv_conn, protocol_by_family(srv_conn->addr.to.ss_family), xprt_get(XPRT_RAW));
-			if (!objt_conn(s->si[1].end) || !objt_conn(s->si[1].end)->ctrl)
+			if (!objt_cs(s->si[1].end) || !objt_cs(s->si[1].end)->conn->ctrl)
 				return SF_ERR_INTERNAL;
-			conn_install_mux(srv_conn, &mux_pt_ops, srv_conn);
+			/* XXX: Pick the right mux, when we finally have one */
+			conn_install_mux(srv_conn, &mux_pt_ops, srv_cs);
 		}
 		else
 			return SF_ERR_INTERNAL;  /* how did we get there ? */
@@ -1182,13 +1188,13 @@ int connect_server(struct stream *s)
 				conn_get_to_addr(cli_conn);
 		}
 
-		si_attach_conn(&s->si[1], srv_conn);
+		si_attach_cs(&s->si[1], srv_cs);
 
 		assign_tproxy_address(s);
 	}
 	else {
 		/* the connection is being reused, just re-attach it */
-		si_attach_conn(&s->si[1], srv_conn);
+		si_attach_cs(&s->si[1], srv_cs);
 		s->flags |= SF_SRV_REUSED;
 	}
 
diff --git a/src/checks.c b/src/checks.c
index b717d3870..aff5ff3ea 100644
--- a/src/checks.c
+++ b/src/checks.c
@@ -582,7 +582,8 @@ static int retrieve_errno_from_socket(struct connection *conn)
  */
 static void chk_report_conn_err(struct check *check, int errno_bck, int expired)
 {
-	struct connection *conn = check->conn;
+	struct conn_stream *cs = check->cs;
+	struct connection *conn = cs_conn(cs);
 	const char *err_msg;
 	struct chunk *chk;
 	int step;
@@ -705,9 +706,10 @@ static void chk_report_conn_err(struct check *check, int errno_bck, int expired)
  * it sends the request. In other cases, it calls set_server_check_status()
  * to set check->status, check->duration and check->result.
  */
-static void event_srv_chk_w(struct connection *conn)
+static void event_srv_chk_w(struct conn_stream *cs)
 {
-	struct check *check = conn->owner;
+	struct connection *conn = cs->conn;
+	struct check *check = cs->data;
 	struct server *s = check->server;
 	struct task *t = check->task;
 
@@ -719,7 +721,7 @@ static void event_srv_chk_w(struct connection *conn)
 
 	if (retrieve_errno_from_socket(conn)) {
 		chk_report_conn_err(check, errno, 0);
-		__conn_xprt_stop_both(conn);
+		__cs_stop_both(cs);
 		goto out_wakeup;
 	}
 
@@ -741,10 +743,10 @@ static void event_srv_chk_w(struct connection *conn)
 		return;
 
 	if (check->bo->o) {
-		conn->xprt->snd_buf(conn, check->bo, 0);
+		conn->mux->snd_buf(cs, check->bo, 0);
 		if (conn->flags & CO_FL_ERROR) {
 			chk_report_conn_err(check, errno, 0);
-			__conn_xprt_stop_both(conn);
+			__cs_stop_both(cs);
 			goto out_wakeup;
 		}
 		if (check->bo->o)
@@ -761,7 +763,7 @@ static void event_srv_chk_w(struct connection *conn)
  out_wakeup:
 	task_wakeup(t, TASK_WOKEN_IO);
  out_nowake:
-	__conn_xprt_stop_send(conn);   /* nothing more to write */
+	__cs_stop_send(cs);   /* nothing more to write */
 }
 
 /*
@@ -778,9 +780,10 @@ static void event_srv_chk_w(struct connection *conn)
  * call it with a proper error status like HCHK_STATUS_L7STS, HCHK_STATUS_L6RSP,
  * etc.
  */
-static void event_srv_chk_r(struct connection *conn)
+static void event_srv_chk_r(struct conn_stream *cs)
 {
-	struct check *check = conn->owner;
+	struct connection *conn = cs->conn;
+	struct check *check = cs->data;
 	struct server *s = check->server;
 	struct task *t = check->task;
 	char *desc;
@@ -815,7 +818,7 @@ static void event_srv_chk_r(struct connection *conn)
 
 	done = 0;
 
-	conn->xprt->rcv_buf(conn, check->bi, check->bi->size);
+	conn->mux->rcv_buf(cs, check->bi, check->bi->size);
 	if (conn->flags & (CO_FL_ERROR | CO_FL_SOCK_RD_SH)) {
 		done = 1;
 		if ((conn->flags & CO_FL_ERROR) && !check->bi->i) {
@@ -1339,8 +1342,8 @@ static void event_srv_chk_r(struct connection *conn)
 	 * range quickly.  To avoid sending RSTs all the time, we first try to
 	 * drain pending data.
 	 */
-	__conn_xprt_stop_both(conn);
-	conn_xprt_shutw(conn);
+	__cs_stop_both(cs);
+	cs_shutw(cs);
 
 	/* OK, let's not stay here forever */
 	if (check->result == CHK_RES_FAILED)
@@ -1350,7 +1353,7 @@ static void event_srv_chk_r(struct connection *conn)
 	return;
 
  wait_more_data:
-	__conn_xprt_want_recv(conn);
+	__cs_want_recv(cs);
 }
 
 /*
@@ -1359,15 +1362,17 @@ static void event_srv_chk_r(struct connection *conn)
  * It returns 0 on normal cases, <0 if at least one close() has happened on the
  * connection (eg: reconnect).
  */
-static int wake_srv_chk(struct connection *conn)
+static int wake_srv_chk(struct conn_stream *cs)
 {
-	struct check *check = conn->owner;
+	struct connection *conn = cs->conn;
+	struct check *check = cs->data;
 	int ret = 0;
 
 	/* we may have to make progress on the TCP checks */
 	if (check->type == PR_O2_TCPCHK_CHK) {
 		ret = tcpcheck_main(check);
-		conn = check->conn;
+		cs = check->cs;
+		conn = cs_conn(cs);
 	}
 
 	if (unlikely(conn->flags & CO_FL_ERROR)) {
@@ -1378,8 +1383,7 @@ static int wake_srv_chk(struct connection *conn)
 		 * we expect errno to still be valid.
 		 */
 		chk_report_conn_err(check, errno, 0);
-
-		__conn_xprt_stop_both(conn);
+		__cs_stop_both(cs);
 		task_wakeup(check->task, TASK_WOKEN_IO);
 	}
 	else if (!(conn->flags & (CO_FL_XPRT_RD_ENA|CO_FL_XPRT_WR_ENA|CO_FL_HANDSHAKE))) {
@@ -1478,7 +1482,8 @@ static int connect_conn_chk(struct task *t)
 {
 	struct check *check = t->context;
 	struct server *s = check->server;
-	struct connection *conn = check->conn;
+	struct conn_stream *cs = check->cs;
+	struct connection *conn = cs_conn(cs);
 	struct protocol *proto;
 	struct tcpcheck_rule *tcp_rule = NULL;
 	int ret;
@@ -1535,9 +1540,10 @@ static int connect_conn_chk(struct task *t)
 	}
 
 	/* prepare a new connection */
-	conn = check->conn = conn_new();
-	if (!check->conn)
+	cs = check->cs = cs_new(NULL);
+	if (!check->cs)
 		return SF_ERR_RESOURCE;
+	conn = cs->conn;
 
 	if (is_addr(&check->addr)) {
 		/* we'll connect to the check addr specified on the server */
@@ -1553,7 +1559,7 @@ static int connect_conn_chk(struct task *t)
 
 		i = srv_check_healthcheck_port(check);
 		if (i == 0) {
-			conn->owner = check;
+			cs->data = check;
 			return SF_ERR_CHK_PORT;
 		}
 
@@ -1563,8 +1569,8 @@ static int connect_conn_chk(struct task *t)
 	proto = protocol_by_family(conn->addr.to.ss_family);
 
 	conn_prepare(conn, proto, check->xprt);
-	conn_install_mux(conn, &mux_pt_ops, conn);
-	conn_attach(conn, check, &check_conn_cb);
+	conn_install_mux(conn, &mux_pt_ops, cs);
+	cs_attach(cs, check, &check_conn_cb);
 	conn->target = &s->obj_type;
 
 	/* no client address */
@@ -2077,7 +2083,8 @@ static struct task *process_chk_conn(struct task *t)
 {
 	struct check *check = t->context;
 	struct server *s = check->server;
-	struct connection *conn = check->conn;
+	struct conn_stream *cs = check->cs;
+	struct connection *conn = cs_conn(cs);
 	int rv;
 	int ret;
 	int expired = tick_is_expired(t->expire, now_ms);
@@ -2105,7 +2112,8 @@ static struct task *process_chk_conn(struct task *t)
 		check->bo->o = 0;
 
 		ret = connect_conn_chk(t);
-		conn = check->conn;
+		cs = check->cs;
+		conn = cs_conn(cs);
 
 		switch (ret) {
 		case SF_ERR_UP:
@@ -2123,7 +2131,7 @@ static struct task *process_chk_conn(struct task *t)
 			}
 
 			if (check->type)
-				conn_xprt_want_recv(conn);   /* prepare for reading a possible reply */
+				cs_want_recv(cs);   /* prepare for reading a possible reply */
 
 			task_set_affinity(t, tid_bit);
 			goto reschedule;
@@ -2147,9 +2155,10 @@ static struct task *process_chk_conn(struct task *t)
 		}
 
 		/* here, we have seen a synchronous error, no fd was allocated */
-		if (conn) {
-			conn_free(conn);
-			check->conn = conn = NULL;
+		if (cs) {
+			cs_destroy(cs);
+			cs = check->cs = NULL;
+			conn = NULL;
 		}
 
 		check->state &= ~CHK_ST_INPROGRESS;
@@ -2201,8 +2210,9 @@ static struct task *process_chk_conn(struct task *t)
 		}
 
 		if (conn) {
-			conn_free(conn);
-			check->conn = conn = NULL;
+			cs_destroy(cs);
+			cs = check->cs = NULL;
+			conn = NULL;
 		}
 
 		if (check->result == CHK_RES_FAILED) {
@@ -2550,7 +2560,8 @@ static int tcpcheck_main(struct check *check)
 	char *contentptr, *comment;
 	struct tcpcheck_rule *next;
 	int done = 0, ret = 0, step = 0;
-	struct connection *conn = check->conn;
+	struct conn_stream *cs = check->cs;
+	struct connection *conn = cs_conn(cs);
 	struct server *s = check->server;
 	struct task *t = check->task;
 	struct list *head = check->tcpcheck_rules;
@@ -2619,8 +2630,8 @@ static int tcpcheck_main(struct check *check)
 	}
 
 	/* It's only the rules which will enable send/recv */
-	if (conn)
-		__conn_xprt_stop_both(conn);
+	if (cs)
+		cs_stop_both(cs);
 
 	while (1) {
 		/* We have to try to flush the output buffer before reading, at
@@ -2633,11 +2644,11 @@ static int tcpcheck_main(struct check *check)
 		     check->current_step->action != TCPCHK_ACT_SEND ||
 		     check->current_step->string_len >= buffer_total_space(check->bo))) {
 
-			__conn_xprt_want_send(conn);
-			if (conn->xprt->snd_buf(conn, check->bo, 0) <= 0) {
+			__cs_want_send(cs);
+			if (conn->mux->snd_buf(cs, check->bo, 0) <= 0) {
 				if (conn->flags & CO_FL_ERROR) {
 					chk_report_conn_err(check, errno, 0);
-					__conn_xprt_stop_both(conn);
+					__cs_stop_both(cs);
 					goto out_end_tcpcheck;
 				}
 				break;
@@ -2673,8 +2684,9 @@ static int tcpcheck_main(struct check *check)
 			 *   2: try to get a new connection
 			 *   3: release and replace the old one on success
 			 */
-			if (check->conn) {
-				conn_full_close(check->conn);
+			if (check->cs) {
+				/* XXX: need to kill all CS here as well but not to free them yet */
+				conn_full_close(check->cs->conn);
 				retcode = -1; /* do not reuse the fd! */
 			}
 
@@ -2682,8 +2694,8 @@ static int tcpcheck_main(struct check *check)
 			check->last_started_step = check->current_step;
 
 			/* prepare new connection */
-			conn = conn_new();
-			if (!conn) {
+			cs = cs_new(NULL);
+			if (!cs) {
 				step = tcpcheck_get_step_id(check);
 				chunk_printf(&trash, "TCPCHK error allocating connection at step %d", step);
 				comment = tcpcheck_get_step_comment(check, step);
@@ -2694,11 +2706,15 @@ static int tcpcheck_main(struct check *check)
 				return retcode;
 			}
 
-			if (check->conn)
-				conn_free(check->conn);
-			check->conn = conn;
+			if (check->cs) {
+				if (check->cs->conn)
+					conn_free(check->cs->conn);
+				cs_free(check->cs);
+			}
 
-			conn_attach(conn, check, &check_conn_cb);
+			check->cs = cs;
+			conn = cs->conn;
+			cs_attach(cs, check, &check_conn_cb);
 			conn->target = &s->obj_type;
 
 			/* no client address */
@@ -2727,7 +2743,7 @@ static int tcpcheck_main(struct check *check)
 				xprt = xprt_get(XPRT_RAW);
 			}
 			conn_prepare(conn, proto, xprt);
-			conn_install_mux(conn, &mux_pt_ops, conn);
+			conn_install_mux(conn, &mux_pt_ops, cs);
 
 			ret = SF_ERR_INTERNAL;
 			if (proto->connect)
@@ -2860,8 +2876,8 @@ static int tcpcheck_main(struct check *check)
 			if (unlikely(check->result == CHK_RES_FAILED))
 				goto out_end_tcpcheck;
 
-			__conn_xprt_want_recv(conn);
-			if (conn->xprt->rcv_buf(conn, check->bi, check->bi->size) <= 0) {
+			__cs_want_recv(cs);
+			if (conn->mux->rcv_buf(cs, check->bi, check->bi->size) <= 0) {
 				if (conn->flags & (CO_FL_ERROR | CO_FL_SOCK_RD_SH)) {
 					done = 1;
 					if ((conn->flags & CO_FL_ERROR) && !check->bi->i) {
@@ -2958,7 +2974,7 @@ static int tcpcheck_main(struct check *check)
 
 					if (check->current_step->action == TCPCHK_ACT_EXPECT)
 						goto tcpcheck_expect;
-					__conn_xprt_stop_recv(conn);
+					__cs_stop_recv(cs);
 				}
 			}
 			else {
@@ -2978,7 +2994,7 @@ static int tcpcheck_main(struct check *check)
 
 					if (check->current_step->action == TCPCHK_ACT_EXPECT)
 						goto tcpcheck_expect;
-					__conn_xprt_stop_recv(conn);
+					__cs_stop_recv(cs);
 				}
 				/* not matched but was supposed to => ERROR */
 				else {
@@ -3012,11 +3028,11 @@ static int tcpcheck_main(struct check *check)
 
 	/* warning, current_step may now point to the head */
 	if (check->bo->o)
-		__conn_xprt_want_send(conn);
+		__cs_want_send(cs);
 
 	if (&check->current_step->list != head &&
 	    check->current_step->action == TCPCHK_ACT_EXPECT)
-		__conn_xprt_want_recv(conn);
+		__cs_want_recv(cs);
 	return retcode;
 
  out_end_tcpcheck:
@@ -3030,7 +3046,7 @@ static int tcpcheck_main(struct check *check)
 	if (check->result == CHK_RES_FAILED)
 		conn->flags |= CO_FL_ERROR;
 
-	__conn_xprt_stop_both(conn);
+	__cs_stop_both(cs);
 	return retcode;
 }
 
@@ -3049,7 +3065,6 @@ const char *init_check(struct check *check, int type)
 		return "out of memory while allocating check buffer";
 	}
 	check->bo->size = global.tune.chksize;
-
 	return NULL;
 }
 
@@ -3059,8 +3074,10 @@ void free_check(struct check *check)
 	check->bi = NULL;
 	free(check->bo);
 	check->bo = NULL;
-	free(check->conn);
-	check->conn = NULL;
+	free(check->cs->conn);
+	check->cs->conn = NULL;
+	cs_free(check->cs);
+	check->cs = NULL;
 }
 
 void email_alert_free(struct email_alert *alert)
diff --git a/src/cli.c b/src/cli.c
index 9ca8e1fcf..b546fd02b 100644
--- a/src/cli.c
+++ b/src/cli.c
@@ -1268,7 +1268,7 @@ static int _getsocks(char **args, struct appctx *appctx, void *private)
 	struct cmsghdr *cmsg;
 	struct stream_interface *si = appctx->owner;
 	struct stream *s = si_strm(si);
-	struct connection *remote = objt_conn(si_opposite(si)->end);
+	struct connection *remote = cs_conn(objt_cs(si_opposite(si)->end));
 	struct msghdr msghdr;
 	struct iovec iov;
 	struct timeval tv = { .tv_sec = 1, .tv_usec = 0 };
diff --git a/src/frontend.c b/src/frontend.c
index e03e0995e..24fc0c147 100644
--- a/src/frontend.c
+++ b/src/frontend.c
@@ -101,7 +101,7 @@ int frontend_accept(struct stream *s)
 
 		/* try to report the ALPN value when available (also works for NPN) */
 
-		if (conn && conn->owner == &s->si[0]) {
+		if (conn && conn == cs_conn(objt_cs(s->si[0].end))) {
 			if (conn_get_alpn(conn, &alpn_str, &alpn_len) && alpn_str) {
 				int len = MIN(alpn_len, sizeof(alpn) - 1);
 				memcpy(alpn, alpn_str, len);
diff --git a/src/hlua.c b/src/hlua.c
index 4911204a5..761fa7f3e 100644
--- a/src/hlua.c
+++ b/src/hlua.c
@@ -1521,7 +1521,7 @@ __LJMP static struct hlua_socket *hlua_checksocket(lua_State *L, int ud)
 static void hlua_socket_handler(struct appctx *appctx)
 {
 	struct stream_interface *si = appctx->owner;
-	struct connection *c = objt_conn(si_opposite(si)->end);
+	struct connection *c = cs_conn(objt_cs(si_opposite(si)->end));
 
 	if (appctx->ctx.hlua_cosocket.die) {
 		si_shutw(si);
@@ -2167,7 +2167,7 @@ __LJMP static int hlua_socket_getpeername(struct lua_State *L)
 	si = appctx->owner;
 	s = si_strm(si);
 
-	conn = objt_conn(s->si[1].end);
+	conn = cs_conn(objt_cs(s->si[1].end));
 	if (!conn) {
 		xref_unlock(&socket->xref, peer);
 		lua_pushnil(L);
@@ -2217,7 +2217,7 @@ static int hlua_socket_getsockname(struct lua_State *L)
 	si = appctx->owner;
 	s = si_strm(si);
 
-	conn = objt_conn(s->si[1].end);
+	conn = cs_conn(objt_cs(s->si[1].end));
 	if (!conn) {
 		xref_unlock(&socket->xref, peer);
 		lua_pushnil(L);
@@ -2346,7 +2346,7 @@ __LJMP static int hlua_socket_connect(struct lua_State *L)
 	s = si_strm(si);
 
 	/* Initialise connection. */
-	conn = si_alloc_conn(&s->si[1]);
+	conn = cs_conn(si_alloc_cs(&s->si[1], NULL));
 	if (!conn) {
 		xref_unlock(&socket->xref, peer);
 		WILL_LJMP(luaL_error(L, "connect: internal error"));
diff --git a/src/log.c b/src/log.c
index 773662b2b..88e0d07a2 100644
--- a/src/log.c
+++ b/src/log.c
@@ -1525,7 +1525,7 @@ int build_logline(struct stream *s, char *dst, size_t maxsize, struct list *list
 				break;
 
 			case LOG_FMT_BACKENDIP:  // %bi
-				conn = objt_conn(s->si[1].end);
+				conn = cs_conn(objt_cs(s->si[1].end));
 				if (conn)
 					ret = lf_ip(tmplog, (struct sockaddr *)&conn->addr.from, dst + maxsize - tmplog, tmp);
 				else
@@ -1538,7 +1538,7 @@ int build_logline(struct stream *s, char *dst, size_t maxsize, struct list *list
 				break;
 
 			case LOG_FMT_BACKENDPORT:  // %bp
-				conn = objt_conn(s->si[1].end);
+				conn = cs_conn(objt_cs(s->si[1].end));
 				if (conn)
 					ret = lf_port(tmplog, (struct sockaddr *)&conn->addr.from, dst + maxsize - tmplog, tmp);
 				else
@@ -1551,7 +1551,7 @@ int build_logline(struct stream *s, char *dst, size_t maxsize, struct list *list
 				break;
 
 			case LOG_FMT_SERVERIP: // %si
-				conn = objt_conn(s->si[1].end);
+				conn = cs_conn(objt_cs(s->si[1].end));
 				if (conn)
 					ret = lf_ip(tmplog, (struct sockaddr *)&conn->addr.to, dst + maxsize - tmplog, tmp);
 				else
@@ -1564,7 +1564,7 @@ int build_logline(struct stream *s, char *dst, size_t maxsize, struct list *list
 				break;
 
 			case LOG_FMT_SERVERPORT: // %sp
-				conn = objt_conn(s->si[1].end);
+				conn = cs_conn(objt_cs(s->si[1].end));
 				if (conn)
 					ret = lf_port(tmplog, (struct sockaddr *)&conn->addr.to, dst + maxsize - tmplog, tmp);
 				else
diff --git a/src/mux_pt.c b/src/mux_pt.c
index 48a676f8b..2a83eb4c7 100644
--- a/src/mux_pt.c
+++ b/src/mux_pt.c
@@ -14,17 +14,31 @@
 #include <proto/connection.h>
 #include <proto/stream.h>
 
-/* Initialize the mux once it's attached. If conn->mux_ctx is NULL, it is
- * assumed that no data layer has yet been instanciated so the mux is
- * attached to an incoming connection and will instanciate a new stream. If
- * conn->mux_ctx exists, it is assumed that it is an outgoing connection
- * requested for this context. Returns < 0 on error.
+/* Initialize the mux once it's attached. It is expected that conn->mux_ctx
+ * points to the existing conn_stream (for outgoing connections) or NULL (for
+ * incoming ones, in which case one will be allocated and a new stream will be
+ * instanciated). Returns < 0 on error.
  */
 static int mux_pt_init(struct connection *conn)
 {
-	if (!conn->mux_ctx)
-		return stream_create_from_conn(conn);
+	struct conn_stream *cs = conn->mux_ctx;
+
+	if (!cs) {
+		cs = cs_new(conn);
+		if (!cs)
+			goto fail;
+
+		if (stream_create_from_cs(cs) < 0)
+			goto fail_free;
+
+		conn->mux_ctx = cs;
+	}
 	return 0;
+
+ fail_free:
+	cs_free(cs);
+ fail:
+	return -1;
 }
 
 /* callback to be used by default for the pass-through mux. It calls the data
@@ -32,7 +46,13 @@ static int mux_pt_init(struct connection *conn)
  */
 static int mux_pt_wake(struct connection *conn)
 {
-	return conn->data->wake ? conn->data->wake(conn) : 0;
+	struct conn_stream *cs = conn->mux_ctx;
+	int ret;
+
+	ret = cs->data_cb->wake ? cs->data_cb->wake(cs) : 0;
+
+	cs_update_mux_polling(cs);
+	return (ret);
 }
 
 /* callback used to update the mux's polling flags after changing a cs' status.
@@ -60,7 +80,12 @@ static void mux_pt_update_poll(struct conn_stream *cs)
  */
 static void mux_pt_recv(struct connection *conn)
 {
-	conn->data->recv(conn);
+	struct conn_stream *cs = conn->mux_ctx;
+
+	if (conn_xprt_read0_pending(conn))
+		cs->flags |= CS_FL_EOS;
+	cs->data_cb->recv(cs);
+	cs_update_mux_polling(cs);
 }
 
 /* callback to be used by default for the pass-through mux. It simply calls the
@@ -68,7 +93,10 @@ static void mux_pt_recv(struct connection *conn)
  */
 static void mux_pt_send(struct connection *conn)
 {
-	conn->data->send(conn);
+	struct conn_stream *cs = conn->mux_ctx;
+
+	cs->data_cb->send(cs);
+	cs_update_mux_polling(cs);
 }
 
 /*
diff --git a/src/peers.c b/src/peers.c
index d7705ea76..9419afe4e 100644
--- a/src/peers.c
+++ b/src/peers.c
@@ -1871,6 +1871,7 @@ static struct appctx *peer_session_create(struct peers *peers, struct peer *peer
 	struct session *sess;
 	struct stream *s;
 	struct connection *conn;
+	struct conn_stream *cs;
 
 	peer->reconnect = tick_add(now_ms, MS_TO_TICKS(5000));
 	peer->statuscode = PEER_SESS_SC_CONNECTCODE;
@@ -1912,9 +1913,12 @@ static struct appctx *peer_session_create(struct peers *peers, struct peer *peer
 	if (unlikely((conn = conn_new()) == NULL))
 		goto out_free_strm;
 
+	if (unlikely((cs = cs_new(conn)) == NULL))
+		goto out_free_conn;
+
 	conn_prepare(conn, peer->proto, peer->xprt);
-	conn_install_mux(conn, &mux_pt_ops, conn);
-	si_attach_conn(&s->si[1], conn);
+	conn_install_mux(conn, &mux_pt_ops, cs);
+	si_attach_cs(&s->si[1], cs);
 
 	conn->target = s->target = &s->be->obj_type;
 	memcpy(&conn->addr.to, &peer->addr, sizeof(conn->addr.to));
@@ -1928,6 +1932,8 @@ static struct appctx *peer_session_create(struct peers *peers, struct peer *peer
 	return appctx;
 
 	/* Error unrolling */
+ out_free_conn:
+	conn_free(conn);
  out_free_strm:
 	LIST_DEL(&s->list);
 	pool_free2(pool2_stream, s);
diff --git a/src/proto_http.c b/src/proto_http.c
index ca9918896..8d813d32a 100644
--- a/src/proto_http.c
+++ b/src/proto_http.c
@@ -3662,7 +3662,7 @@ int http_process_request(struct stream *s, struct channel *req, int an_bit)
 		char *path;
 
 		/* Note that for now we don't reuse existing proxy connections */
-		if (unlikely((conn = si_alloc_conn(&s->si[1])) == NULL)) {
+		if (unlikely((conn = cs_conn(si_alloc_cs(&s->si[1], NULL))) == NULL)) {
 			txn->req.err_state = txn->req.msg_state;
 			txn->req.msg_state = HTTP_MSG_ERROR;
 			txn->status = 500;
@@ -4212,6 +4212,7 @@ void http_end_txn_clean_session(struct stream *s)
 	int prev_status = s->txn->status;
 	struct proxy *fe = strm_fe(s);
 	struct proxy *be = s->be;
+	struct conn_stream *cs;
 	struct connection *srv_conn;
 	struct server *srv;
 	unsigned int prev_flags = s->txn->flags;
@@ -4221,7 +4222,14 @@ void http_end_txn_clean_session(struct stream *s)
 	 * flags. We also need a more accurate method for computing per-request
 	 * data.
 	 */
-	srv_conn = objt_conn(s->si[1].end);
+	/*
+	 * XXX cognet: This is probably wrong, this is killing a whole
+	 * connection, in the new world order, we probably want to just kill
+	 * the stream, this is to be revisited the day we handle multiple
+	 * streams in one server connection.
+	 */
+	cs = objt_cs(s->si[1].end);
+	srv_conn = cs_conn(cs);
 
 	/* unless we're doing keep-alive, we want to quickly close the connection
 	 * to the server.
@@ -4364,17 +4372,17 @@ void http_end_txn_clean_session(struct stream *s)
 	if (srv_conn && LIST_ISEMPTY(&srv_conn->list)) {
 		srv = objt_server(srv_conn->target);
 		if (!srv)
-			si_idle_conn(&s->si[1], NULL);
+			si_idle_cs(&s->si[1], NULL);
 		else if (srv_conn->flags & CO_FL_PRIVATE)
-			si_idle_conn(&s->si[1], (srv->priv_conns ? &srv->priv_conns[tid] : NULL));
+			si_idle_cs(&s->si[1], (srv->priv_conns ? &srv->priv_conns[tid] : NULL));
 		else if (prev_flags & TX_NOT_FIRST)
 			/* note: we check the request, not the connection, but
 			 * this is valid for strategies SAFE and AGGR, and in
 			 * case of ALWS, we don't care anyway.
 			 */
-			si_idle_conn(&s->si[1], (srv->safe_conns ? &srv->safe_conns[tid] : NULL));
+			si_idle_cs(&s->si[1], (srv->safe_conns ? &srv->safe_conns[tid] : NULL));
 		else
-			si_idle_conn(&s->si[1], (srv->idle_conns ? &srv->idle_conns[tid] : NULL));
+			si_idle_cs(&s->si[1], (srv->idle_conns ? &srv->idle_conns[tid] : NULL));
 	}
 	s->req.analysers = strm_li(s) ? strm_li(s)->analysers : 0;
 	s->res.analysers = 0;
@@ -7936,7 +7944,7 @@ void debug_hdr(const char *dir, struct stream *s, const char *start, const char
 	chunk_printf(&trash, "%08x:%s.%s[%04x:%04x]: ", s->uniq_id, s->be->id,
 		      dir,
 		     objt_conn(sess->origin) ? (unsigned short)objt_conn(sess->origin)->handle.fd : -1,
-		     objt_conn(s->si[1].end) ? (unsigned short)objt_conn(s->si[1].end)->handle.fd : -1);
+		     objt_cs(s->si[1].end) ? (unsigned short)objt_cs(s->si[1].end)->conn->handle.fd : -1);
 
 	for (max = 0; start + max < end; max++)
 		if (start[max] == '\r' || start[max] == '\n')
diff --git a/src/proto_tcp.c b/src/proto_tcp.c
index d5345ee3c..5badda7e0 100644
--- a/src/proto_tcp.c
+++ b/src/proto_tcp.c
@@ -1598,11 +1598,11 @@ static inline int get_tcp_info(const struct arg *args, struct sample *smp,
 	/* get the object associated with the stream interface.The
 	 * object can be other thing than a connection. For example,
 	 * it be a appctx. */
-	conn = objt_conn(smp->strm->si[dir].end);
+	conn = cs_conn(objt_cs(smp->strm->si[dir].end));
 	if (!conn)
 		return 0;
 
-	/* The fd may not be avalaible for the tcp_info struct, and the
+	/* The fd may not be available for the tcp_info struct, and the
 	  syscal can fail. */
 	optlen = sizeof(info);
 	if (getsockopt(conn->handle.fd, SOL_TCP, TCP_INFO, &info, &optlen) == -1)
diff --git a/src/stream.c b/src/stream.c
index 4808cfa0d..722d2f4fd 100644
--- a/src/stream.c
+++ b/src/stream.c
@@ -74,11 +74,11 @@ static struct list service_keywords = LIST_HEAD_INIT(service_keywords);
  * valid right after the handshake, before the connection's data layer is
  * initialized, because it relies on the session to be in conn->owner.
  */
-int stream_create_from_conn(struct connection *conn)
+int stream_create_from_cs(struct conn_stream *cs)
 {
 	struct stream *strm;
 
-	strm = stream_new(conn->owner, &conn->obj_type);
+	strm = stream_new(cs->conn->owner, &cs->obj_type);
 	if (strm == NULL)
 		return -1;
 
@@ -99,7 +99,7 @@ struct stream *stream_new(struct session *sess, enum obj_type *origin)
 {
 	struct stream *s;
 	struct task *t;
-	struct connection *conn = objt_conn(origin);
+	struct conn_stream *cs  = objt_cs(origin);
 	struct appctx *appctx   = objt_appctx(origin);
 
 	if (unlikely((s = pool_alloc2(pool2_stream)) == NULL))
@@ -198,8 +198,8 @@ struct stream *stream_new(struct session *sess, enum obj_type *origin)
 	s->si[0].hcto = sess->fe->timeout.clientfin;
 
 	/* attach the incoming connection to the stream interface now. */
-	if (conn)
-		si_attach_conn(&s->si[0], conn);
+	if (cs)
+		si_attach_cs(&s->si[0], cs);
 	else if (appctx)
 		si_attach_appctx(&s->si[0], appctx);
 
@@ -261,8 +261,8 @@ struct stream *stream_new(struct session *sess, enum obj_type *origin)
 		goto out_fail_accept;
 
 	/* finish initialization of the accepted file descriptor */
-	if (conn)
-		conn_xprt_want_recv(conn);
+	if (cs)
+		cs_want_recv(cs);
 	else if (appctx)
 		si_applet_want_get(&s->si[0]);
 
@@ -295,7 +295,8 @@ static void stream_free(struct stream *s)
 	struct session *sess = strm_sess(s);
 	struct proxy *fe = sess->fe;
 	struct bref *bref, *back;
-	struct connection *cli_conn = objt_conn(s->si[0].end);
+	struct conn_stream *cli_cs = objt_cs(s->si[0].end);
+	struct connection *cli_conn = cs_conn(cli_cs);
 	int i;
 
 	if (s->pend_pos)
@@ -343,6 +344,7 @@ static void stream_free(struct stream *s)
 		http_end_txn(s);
 
 	/* ensure the client-side transport layer is destroyed */
+	/* XXX cognet: wrong for multiple streams in one connection */
 	if (cli_conn) {
 		conn_stop_tracking(cli_conn);
 		conn_full_close(cli_conn);
@@ -577,7 +579,7 @@ static int sess_update_st_con_tcp(struct stream *s)
 	struct stream_interface *si = &s->si[1];
 	struct channel *req = &s->req;
 	struct channel *rep = &s->res;
-	struct connection *srv_conn = __objt_conn(si->end);
+	struct connection *srv_conn = __objt_cs(si->end)->conn;
 
 	/* If we got an error, or if nothing happened and the connection timed
 	 * out, we must give up. The CER state handler will take care of retry
@@ -597,6 +599,9 @@ static int sess_update_st_con_tcp(struct stream *s)
 		si->exp   = TICK_ETERNITY;
 		si->state = SI_ST_CER;
 
+		/* XXX cognet: do we really want to kill the connection here ?
+		 * Probably not for multiple streams.
+		 */
 		conn_full_close(srv_conn);
 
 		if (si->err_type)
@@ -647,7 +652,8 @@ static int sess_update_st_con_tcp(struct stream *s)
 static int sess_update_st_cer(struct stream *s)
 {
 	struct stream_interface *si = &s->si[1];
-	struct connection *conn = objt_conn(si->end);
+	struct conn_stream *cs = objt_cs(si->end);
+	struct connection *conn = cs_conn(cs);
 
 	/* we probably have to release last stream from the server */
 	if (objt_server(s->target)) {
@@ -812,7 +818,7 @@ static void sess_establish(struct stream *s)
 		req->flags |= CF_WAKE_ONCE;
 		req->flags &= ~CF_WAKE_CONNECT;
 	}
-	if (objt_conn(si->end)) {
+	if (objt_cs(si->end)) {
 		/* real connections have timeouts */
 		req->wto = s->be->timeout.server;
 		rep->rto = s->be->timeout.server;
@@ -2111,8 +2117,8 @@ struct task *process_stream(struct task *t)
 	if (!(req->flags & (CF_KERN_SPLICING|CF_SHUTR)) &&
 	    req->to_forward &&
 	    (global.tune.options & GTUNE_USE_SPLICE) &&
-	    (objt_conn(si_f->end) && __objt_conn(si_f->end)->xprt && __objt_conn(si_f->end)->xprt->rcv_pipe) &&
-	    (objt_conn(si_b->end) && __objt_conn(si_b->end)->xprt && __objt_conn(si_b->end)->xprt->snd_pipe) &&
+	    (objt_cs(si_f->end) && __objt_cs(si_f->end)->conn->xprt && __objt_cs(si_f->end)->conn->xprt->rcv_pipe) &&
+	    (objt_cs(si_b->end) && __objt_cs(si_b->end)->conn->xprt && __objt_cs(si_b->end)->conn->xprt->snd_pipe) &&
 	    (pipes_used < global.maxpipes) &&
 	    (((sess->fe->options2|s->be->options2) & PR_O2_SPLIC_REQ) ||
 	     (((sess->fe->options2|s->be->options2) & PR_O2_SPLIC_AUT) &&
@@ -2292,8 +2298,8 @@ struct task *process_stream(struct task *t)
 	if (!(res->flags & (CF_KERN_SPLICING|CF_SHUTR)) &&
 	    res->to_forward &&
 	    (global.tune.options & GTUNE_USE_SPLICE) &&
-	    (objt_conn(si_f->end) && __objt_conn(si_f->end)->xprt && __objt_conn(si_f->end)->xprt->snd_pipe) &&
-	    (objt_conn(si_b->end) && __objt_conn(si_b->end)->xprt && __objt_conn(si_b->end)->xprt->rcv_pipe) &&
+	    (objt_cs(si_f->end) && __objt_cs(si_f->end)->conn->xprt && __objt_cs(si_f->end)->conn->xprt->snd_pipe) &&
+	    (objt_cs(si_b->end) && __objt_cs(si_b->end)->conn->xprt && __objt_cs(si_b->end)->conn->xprt->rcv_pipe) &&
 	    (pipes_used < global.maxpipes) &&
 	    (((sess->fe->options2|s->be->options2) & PR_O2_SPLIC_RTR) ||
 	     (((sess->fe->options2|s->be->options2) & PR_O2_SPLIC_AUT) &&
@@ -2361,8 +2367,8 @@ struct task *process_stream(struct task *t)
 		    si_b->prev_state == SI_ST_EST) {
 			chunk_printf(&trash, "%08x:%s.srvcls[%04x:%04x]\n",
 				      s->uniq_id, s->be->id,
-			              objt_conn(si_f->end) ? (unsigned short)objt_conn(si_f->end)->handle.fd : -1,
-			              objt_conn(si_b->end) ? (unsigned short)objt_conn(si_b->end)->handle.fd : -1);
+			              objt_cs(si_f->end) ? (unsigned short)objt_cs(si_f->end)->conn->handle.fd : -1,
+			              objt_cs(si_b->end) ? (unsigned short)objt_cs(si_b->end)->conn->handle.fd : -1);
 			shut_your_big_mouth_gcc(write(1, trash.str, trash.len));
 		}
 
@@ -2370,8 +2376,8 @@ struct task *process_stream(struct task *t)
 		    si_f->prev_state == SI_ST_EST) {
 			chunk_printf(&trash, "%08x:%s.clicls[%04x:%04x]\n",
 				      s->uniq_id, s->be->id,
-			              objt_conn(si_f->end) ? (unsigned short)objt_conn(si_f->end)->handle.fd : -1,
-			              objt_conn(si_b->end) ? (unsigned short)objt_conn(si_b->end)->handle.fd : -1);
+			              objt_cs(si_f->end) ? (unsigned short)objt_cs(si_f->end)->conn->handle.fd : -1,
+			              objt_cs(si_b->end) ? (unsigned short)objt_cs(si_b->end)->conn->handle.fd : -1);
 			shut_your_big_mouth_gcc(write(1, trash.str, trash.len));
 		}
 	}
@@ -2460,8 +2466,8 @@ struct task *process_stream(struct task *t)
 		     (!(global.mode & MODE_QUIET) || (global.mode & MODE_VERBOSE)))) {
 		chunk_printf(&trash, "%08x:%s.closed[%04x:%04x]\n",
 			      s->uniq_id, s->be->id,
-		              objt_conn(si_f->end) ? (unsigned short)objt_conn(si_f->end)->handle.fd : -1,
-		              objt_conn(si_b->end) ? (unsigned short)objt_conn(si_b->end)->handle.fd : -1);
+		              objt_cs(si_f->end) ? (unsigned short)objt_cs(si_f->end)->conn->handle.fd : -1,
+		              objt_cs(si_b->end) ? (unsigned short)objt_cs(si_b->end)->conn->handle.fd : -1);
 		shut_your_big_mouth_gcc(write(1, trash.str, trash.len));
 	}
 
@@ -2692,6 +2698,7 @@ static int stats_dump_full_strm_to_buffer(struct stream_interface *si, struct st
 	struct tm tm;
 	extern const char *monthname[12];
 	char pn[INET6_ADDRSTRLEN];
+	struct conn_stream *cs;
 	struct connection *conn;
 	struct appctx *tmpctx;
 
@@ -2777,7 +2784,9 @@ static int stats_dump_full_strm_to_buffer(struct stream_interface *si, struct st
 		else
 			chunk_appendf(&trash, "  backend=<NONE> (id=-1 mode=-)");
 
-		conn = objt_conn(strm->si[1].end);
+		cs = objt_cs(strm->si[1].end);
+		conn = cs_conn(cs);
+
 		if (conn)
 			conn_get_from_addr(conn);
 
@@ -2869,14 +2878,16 @@ static int stats_dump_full_strm_to_buffer(struct stream_interface *si, struct st
 			                     TICKS_TO_MS(1000)) : "<NEVER>",
 			     strm->si[1].err_type);
 
-		if ((conn = objt_conn(strm->si[0].end)) != NULL) {
+		if ((cs = objt_cs(strm->si[0].end)) != NULL) {
+			conn = cs->conn;
+
 			chunk_appendf(&trash,
 			              "  co0=%p ctrl=%s xprt=%s mux=%s data=%s target=%s:%p\n",
 				      conn,
 				      conn_get_ctrl_name(conn),
 				      conn_get_xprt_name(conn),
 				      conn_get_mux_name(conn),
-				      conn_get_data_name(conn),
+				      cs_get_data_name(cs),
 			              obj_type_name(conn->target),
 			              obj_base_ptr(conn->target));
 
@@ -2898,14 +2909,16 @@ static int stats_dump_full_strm_to_buffer(struct stream_interface *si, struct st
 			              tmpctx->applet->name);
 		}
 
-		if ((conn = objt_conn(strm->si[1].end)) != NULL) {
+		if ((cs = objt_cs(strm->si[1].end)) != NULL) {
+			conn = cs->conn;
+
 			chunk_appendf(&trash,
 			              "  co1=%p ctrl=%s xprt=%s mux=%s data=%s target=%s:%p\n",
 				      conn,
 				      conn_get_ctrl_name(conn),
 				      conn_get_xprt_name(conn),
 				      conn_get_mux_name(conn),
-				      conn_get_data_name(conn),
+				      cs_get_data_name(cs),
 			              obj_type_name(conn->target),
 			              obj_base_ptr(conn->target));
 
@@ -3171,7 +3184,7 @@ static int cli_io_handler_dump_sess(struct appctx *appctx)
 				     human_time(TICKS_TO_MS(curr_strm->res.analyse_exp - now_ms),
 						TICKS_TO_MS(1000)) : "");
 
-			conn = objt_conn(curr_strm->si[0].end);
+			conn = cs_conn(objt_cs(curr_strm->si[0].end));
 			chunk_appendf(&trash,
 				     " s0=[%d,%1xh,fd=%d,ex=%s]",
 				     curr_strm->si[0].state,
@@ -3181,7 +3194,7 @@ static int cli_io_handler_dump_sess(struct appctx *appctx)
 				     human_time(TICKS_TO_MS(curr_strm->si[0].exp - now_ms),
 						TICKS_TO_MS(1000)) : "");
 
-			conn = objt_conn(curr_strm->si[1].end);
+			conn = cs_conn(objt_cs(curr_strm->si[1].end));
 			chunk_appendf(&trash,
 				     " s1=[%d,%1xh,fd=%d,ex=%s]",
 				     curr_strm->si[1].state,
diff --git a/src/stream_interface.c b/src/stream_interface.c
index a5463b751..e9bc83157 100644
--- a/src/stream_interface.c
+++ b/src/stream_interface.c
@@ -30,6 +30,7 @@
 #include <proto/applet.h>
 #include <proto/channel.h>
 #include <proto/connection.h>
+#include <proto/mux_pt.h>
 #include <proto/pipe.h>
 #include <proto/stream.h>
 #include <proto/stream_interface.h>
@@ -50,11 +51,11 @@ static void stream_int_shutr_applet(struct stream_interface *si);
 static void stream_int_shutw_applet(struct stream_interface *si);
 static void stream_int_chk_rcv_applet(struct stream_interface *si);
 static void stream_int_chk_snd_applet(struct stream_interface *si);
-static void si_conn_recv_cb(struct connection *conn);
-static void si_conn_send_cb(struct connection *conn);
-static int si_conn_wake_cb(struct connection *conn);
-static int si_idle_conn_wake_cb(struct connection *conn);
-static void si_idle_conn_null_cb(struct connection *conn);
+static void si_cs_recv_cb(struct conn_stream *cs);
+static void si_cs_send_cb(struct conn_stream *cs);
+static int si_cs_wake_cb(struct conn_stream *cs);
+static int si_idle_conn_wake_cb(struct conn_stream *cs);
+static void si_idle_conn_null_cb(struct conn_stream *cs);
 
 /* stream-interface operations for embedded tasks */
 struct si_ops si_embedded_ops = {
@@ -83,9 +84,9 @@ struct si_ops si_applet_ops = {
 };
 
 struct data_cb si_conn_cb = {
-	.recv    = si_conn_recv_cb,
-	.send    = si_conn_send_cb,
-	.wake    = si_conn_wake_cb,
+	.recv    = si_cs_recv_cb,
+	.send    = si_cs_send_cb,
+	.wake    = si_cs_wake_cb,
 	.name    = "STRM",
 };
 
@@ -337,8 +338,10 @@ int conn_si_send_proxy(struct connection *conn, unsigned int flag)
 	 * we've sent the whole proxy line. Otherwise we use connect().
 	 */
 	while (conn->send_proxy_ofs) {
+		struct conn_stream *cs;
 		int ret;
 
+		cs = conn->mux_ctx;
 		/* The target server expects a PROXY line to be sent first.
 		 * If the send_proxy_ofs is negative, it corresponds to the
 		 * offset to start sending from then end of the proxy string
@@ -348,10 +351,10 @@ int conn_si_send_proxy(struct connection *conn, unsigned int flag)
 		 * is attached to a stream interface. Otherwise we can only
 		 * send a LOCAL line (eg: for use with health checks).
 		 */
-		if (conn->data == &si_conn_cb) {
-			struct stream_interface *si = conn->owner;
-			struct connection *remote = objt_conn(si_opposite(si)->end);
-			ret = make_proxy_line(trash.str, trash.size, objt_server(conn->target), remote);
+		if (conn->mux == &mux_pt_ops && cs->data_cb == &si_conn_cb) {
+			struct stream_interface *si = cs->data;
+			struct conn_stream *remote_cs = objt_cs(si_opposite(si)->end);
+			ret = make_proxy_line(trash.str, trash.size, objt_server(conn->target), remote_cs ? remote_cs->conn : NULL);
 		}
 		else {
 			/* The target server expects a LOCAL line to be sent first. Retrieving
@@ -414,9 +417,9 @@ int conn_si_send_proxy(struct connection *conn, unsigned int flag)
  * It simply sets the CO_FL_SOCK_RD_SH flag so that si_idle_conn_wake_cb()
  * is notified and can kill the connection.
  */
-static void si_idle_conn_null_cb(struct connection *conn)
+static void si_idle_conn_null_cb(struct conn_stream *cs)
 {
-	conn_sock_drain(conn);
+	conn_sock_drain(cs->conn);
 }
 
 /* Callback to be used by connection I/O handlers when some activity is detected
@@ -424,9 +427,10 @@ static void si_idle_conn_null_cb(struct connection *conn)
  * a close was detected on it. It returns 0 if it did nothing serious, or -1 if
  * it killed the connection.
  */
-static int si_idle_conn_wake_cb(struct connection *conn)
+static int si_idle_conn_wake_cb(struct conn_stream *cs)
 {
-	struct stream_interface *si = conn->owner;
+	struct connection *conn = cs->conn;
+	struct stream_interface *si = cs->data;
 
 	if (!conn_ctrl_ready(conn))
 		return 0;
@@ -560,9 +564,10 @@ void stream_int_notify(struct stream_interface *si)
  * connection's polling based on the channels and stream interface's final
  * states. The function always returns 0.
  */
-static int si_conn_wake_cb(struct connection *conn)
+static int si_cs_wake_cb(struct conn_stream *cs)
 {
-	struct stream_interface *si = conn->owner;
+	struct connection *conn = cs->conn;
+	struct stream_interface *si = cs->data;
 	struct channel *ic = si_ic(si);
 	struct channel *oc = si_oc(si);
 
@@ -599,36 +604,37 @@ static int si_conn_wake_cb(struct connection *conn)
 	 * was done above (eg: maybe some buffers got emptied).
 	 */
 	if (channel_is_empty(oc))
-		__conn_xprt_stop_send(conn);
+		__cs_stop_send(cs);
 
 
 	if (si->flags & SI_FL_WAIT_ROOM) {
-		__conn_xprt_stop_recv(conn);
+		__cs_stop_recv(cs);
 	}
 	else if ((ic->flags & (CF_SHUTR|CF_READ_PARTIAL|CF_DONT_READ)) == CF_READ_PARTIAL &&
 		 channel_may_recv(ic)) {
-		__conn_xprt_want_recv(conn);
+		__cs_want_recv(cs);
 	}
 	return 0;
 }
 
 /*
  * This function is called to send buffer data to a stream socket.
- * It calls the transport layer's snd_buf function. It relies on the
+ * It calls the mux layer's snd_buf function. It relies on the
  * caller to commit polling changes. The caller should check conn->flags
  * for errors.
  */
-static void si_conn_send(struct connection *conn)
+static void si_cs_send(struct conn_stream *cs)
 {
-	struct stream_interface *si = conn->owner;
+	struct connection *conn = cs->conn;
+	struct stream_interface *si = cs->data;
 	struct channel *oc = si_oc(si);
 	int ret;
 
 	/* ensure it's only set if a write attempt has succeeded */
 	oc->flags &= ~CF_WRITE_PARTIAL;
 
-	if (oc->pipe && conn->xprt->snd_pipe) {
-		ret = conn->xprt->snd_pipe(conn, oc->pipe);
+	if (oc->pipe && conn->xprt->snd_pipe && conn->mux->snd_pipe) {
+		ret = conn->mux->snd_pipe(cs, oc->pipe);
 		if (ret > 0)
 			oc->flags |= CF_WRITE_PARTIAL | CF_WROTE_DATA;
 
@@ -672,7 +678,7 @@ static void si_conn_send(struct connection *conn)
 		if (oc->flags & CF_STREAMER)
 			send_flag |= CO_SFL_STREAMER;
 
-		ret = conn->xprt->snd_buf(conn, oc->buf, send_flag);
+		ret = conn->mux->snd_buf(cs, oc->buf, send_flag);
 		if (ret > 0) {
 			oc->flags |= CF_WRITE_PARTIAL | CF_WROTE_DATA;
 
@@ -766,25 +772,25 @@ void stream_int_update_conn(struct stream_interface *si)
 {
 	struct channel *ic = si_ic(si);
 	struct channel *oc = si_oc(si);
-	struct connection *conn = __objt_conn(si->end);
+	struct conn_stream *cs = __objt_cs(si->end);
 
 	if (!(ic->flags & CF_SHUTR)) {
 		/* Read not closed */
 		if ((ic->flags & CF_DONT_READ) || !channel_may_recv(ic))
-			__conn_xprt_stop_recv(conn);
+			__cs_stop_recv(cs);
 		else
-			__conn_xprt_want_recv(conn);
+			__cs_want_recv(cs);
 	}
 
 	if (!(oc->flags & CF_SHUTW)) {
 		/* Write not closed */
 		if (channel_is_empty(oc))
-			__conn_xprt_stop_send(conn);
+			__cs_stop_send(cs);
 		else
-			__conn_xprt_want_send(conn);
+			__cs_want_send(cs);
 	}
 
-	conn_cond_update_xprt_polling(conn);
+	cs_update_mux_polling(cs);
 }
 
 /*
@@ -799,7 +805,8 @@ void stream_int_update_conn(struct stream_interface *si)
  */
 static void stream_int_shutr_conn(struct stream_interface *si)
 {
-	struct connection *conn = __objt_conn(si->end);
+	struct conn_stream *cs = __objt_cs(si->end);
+	struct connection *conn = cs->conn;
 	struct channel *ic = si_ic(si);
 
 	ic->flags &= ~CF_SHUTR_NOW;
@@ -813,6 +820,7 @@ static void stream_int_shutr_conn(struct stream_interface *si)
 		return;
 
 	if (si_oc(si)->flags & CF_SHUTW) {
+		/* XXX: should just close cs ? */
 		conn_full_close(conn);
 		si->state = SI_ST_DIS;
 		si->exp = TICK_ETERNITY;
@@ -823,7 +831,7 @@ static void stream_int_shutr_conn(struct stream_interface *si)
 	}
 	else if (conn->ctrl) {
 		/* we want the caller to disable polling on this FD */
-		conn_xprt_stop_recv(conn);
+		cs_stop_recv(cs);
 	}
 }
 
@@ -837,7 +845,8 @@ static void stream_int_shutr_conn(struct stream_interface *si)
  */
 static void stream_int_shutw_conn(struct stream_interface *si)
 {
-	struct connection *conn = __objt_conn(si->end);
+	struct conn_stream *cs = __objt_cs(si->end);
+	struct connection *conn = cs->conn;
 	struct channel *ic = si_ic(si);
 	struct channel *oc = si_oc(si);
 
@@ -865,13 +874,21 @@ static void stream_int_shutw_conn(struct stream_interface *si)
 			/* quick close, the socket is alredy shut anyway */
 		}
 		else if (si->flags & SI_FL_NOLINGER) {
-			/* unclean data-layer shutdown */
-			conn_xprt_shutw_hard(conn);
+			/* unclean data-layer shutdown, typically an aborted request
+			 * or a forwarded shutdown from a client to a server due to
+			 * option abortonclose. No need for the TLS layer to try to
+			 * emit a shutdown message.
+			 */
+			cs_shutw_hard(cs);
 		}
 		else {
-			/* clean data-layer shutdown */
-			conn_xprt_shutw(conn);
-			conn_sock_shutw(conn);
+			/* clean data-layer shutdown. This only happens on the
+			 * frontend side, or on the backend side when forwarding
+			 * a client close in TCP mode or in HTTP TUNNEL mode
+			 * while option abortonclose is set. We want the TLS
+			 * layer to try to signal it to the peer before we close.
+			 */
+			cs_shutw(cs);
 
 			/* If the stream interface is configured to disable half-open
 			 * connections, we'll skip the shutdown(), but only if the
@@ -920,25 +937,23 @@ static void stream_int_shutw_conn(struct stream_interface *si)
 static void stream_int_chk_rcv_conn(struct stream_interface *si)
 {
 	struct channel *ic = si_ic(si);
-	struct connection *conn = __objt_conn(si->end);
+	struct conn_stream *cs = __objt_cs(si->end);
 
 	if (unlikely(si->state > SI_ST_EST || (ic->flags & CF_SHUTR)))
 		return;
 
-	conn_refresh_polling_flags(conn);
-
 	if ((ic->flags & CF_DONT_READ) || !channel_may_recv(ic)) {
 		/* stop reading */
 		if (!(ic->flags & CF_DONT_READ)) /* full */
 			si->flags |= SI_FL_WAIT_ROOM;
-		__conn_xprt_stop_recv(conn);
+		__cs_stop_recv(cs);
 	}
 	else {
 		/* (re)start reading */
 		si->flags &= ~SI_FL_WAIT_ROOM;
-		__conn_xprt_want_recv(conn);
+		__cs_want_recv(cs);
 	}
-	conn_cond_update_xprt_polling(conn);
+	cs_update_mux_polling(cs);
 }
 
 
@@ -950,7 +965,7 @@ static void stream_int_chk_rcv_conn(struct stream_interface *si)
 static void stream_int_chk_snd_conn(struct stream_interface *si)
 {
 	struct channel *oc = si_oc(si);
-	struct connection *conn = __objt_conn(si->end);
+	struct conn_stream *cs = __objt_cs(si->end);
 
 	/* ensure it's only set if a write attempt has succeeded */
 	oc->flags &= ~CF_WRITE_PARTIAL;
@@ -965,7 +980,7 @@ static void stream_int_chk_snd_conn(struct stream_interface *si)
 	    !(si->flags & SI_FL_WAIT_DATA))       /* not waiting for data */
 		return;
 
-	if (conn->flags & CO_FL_XPRT_WR_ENA) {
+	if (cs->flags & CS_FL_DATA_WR_ENA) {
 		/* already subscribed to write notifications, will be called
 		 * anyway, so let's avoid calling it especially if the reader
 		 * is not ready.
@@ -973,16 +988,12 @@ static void stream_int_chk_snd_conn(struct stream_interface *si)
 		return;
 	}
 
-	/* Before calling the data-level operations, we have to prepare
-	 * the polling flags to ensure we properly detect changes.
-	 */
-	conn_refresh_polling_flags(conn);
-	__conn_xprt_want_send(conn);
+	__cs_want_send(cs);
 
-	si_conn_send(conn);
-	if (conn->flags & CO_FL_ERROR) {
+	si_cs_send(cs);
+	if (cs->conn->flags & CO_FL_ERROR) {
 		/* Write error on the file descriptor */
-		__conn_xprt_stop_both(conn);
+		__cs_stop_both(cs);
 		si->flags |= SI_FL_ERR;
 		goto out_wakeup;
 	}
@@ -996,7 +1007,7 @@ static void stream_int_chk_snd_conn(struct stream_interface *si)
 		 * ->o limit was reached. Maybe we just wrote the last
 		 * chunk and need to close.
 		 */
-		__conn_xprt_stop_send(conn);
+		__cs_stop_send(cs);
 		if (((oc->flags & (CF_SHUTW|CF_AUTO_CLOSE|CF_SHUTW_NOW)) ==
 		     (CF_AUTO_CLOSE|CF_SHUTW_NOW)) &&
 		    (si->state == SI_ST_EST)) {
@@ -1012,7 +1023,7 @@ static void stream_int_chk_snd_conn(struct stream_interface *si)
 		/* Otherwise there are remaining data to be sent in the buffer,
 		 * which means we have to poll before doing so.
 		 */
-		__conn_xprt_want_send(conn);
+		__cs_want_send(cs);
 		si->flags &= ~SI_FL_WAIT_DATA;
 		if (!tick_isset(oc->wex))
 			oc->wex = tick_add_ifset(now_ms, oc->wto);
@@ -1052,17 +1063,18 @@ static void stream_int_chk_snd_conn(struct stream_interface *si)
 	}
 
 	/* commit possible polling changes */
-	conn_cond_update_polling(conn);
+	cs_update_mux_polling(cs);
 }
 
 /*
  * This is the callback which is called by the connection layer to receive data
- * into the buffer from the connection. It iterates over the transport layer's
+ * into the buffer from the connection. It iterates over the mux layer's
  * rcv_buf function.
  */
-static void si_conn_recv_cb(struct connection *conn)
+static void si_cs_recv_cb(struct conn_stream *cs)
 {
-	struct stream_interface *si = conn->owner;
+	struct connection *conn = cs->conn;
+	struct stream_interface *si = cs->data;
 	struct channel *ic = si_ic(si);
 	int ret, max, cur_read;
 	int read_poll = MAX_READ_POLL_LOOPS;
@@ -1081,7 +1093,7 @@ static void si_conn_recv_cb(struct connection *conn)
 		return;
 
 	/* stop here if we reached the end of data */
-	if (conn_xprt_read0_pending(conn))
+	if (cs->flags & CS_FL_EOS)
 		goto out_shutdown_r;
 
 	cur_read = 0;
@@ -1101,7 +1113,7 @@ static void si_conn_recv_cb(struct connection *conn)
 	/* First, let's see if we may splice data across the channel without
 	 * using a buffer.
 	 */
-	if (conn->xprt->rcv_pipe &&
+	if (conn->xprt->rcv_pipe && conn->mux->rcv_pipe &&
 	    (ic->pipe || ic->to_forward >= MIN_SPLICE_FORWARD) &&
 	    ic->flags & CF_KERN_SPLICING) {
 		if (buffer_not_empty(ic->buf)) {
@@ -1120,7 +1132,7 @@ static void si_conn_recv_cb(struct connection *conn)
 			}
 		}
 
-		ret = conn->xprt->rcv_pipe(conn, ic->pipe, ic->to_forward);
+		ret = conn->mux->rcv_pipe(cs, ic->pipe, ic->to_forward);
 		if (ret < 0) {
 			/* splice not supported on this end, let's disable it */
 			ic->flags &= ~CF_KERN_SPLICING;
@@ -1135,7 +1147,7 @@ static void si_conn_recv_cb(struct connection *conn)
 			ic->flags |= CF_READ_PARTIAL;
 		}
 
-		if (conn_xprt_read0_pending(conn))
+		if (cs->flags & CS_FL_EOS)
 			goto out_shutdown_r;
 
 		if (conn->flags & CO_FL_ERROR)
@@ -1146,7 +1158,7 @@ static void si_conn_recv_cb(struct connection *conn)
 			 * could soon be full. Let's stop before needing to poll.
 			 */
 			si->flags |= SI_FL_WAIT_ROOM;
-			__conn_xprt_stop_recv(conn);
+			__cs_stop_recv(cs);
 		}
 
 		/* splice not possible (anymore), let's go on on standard copy */
@@ -1177,7 +1189,7 @@ static void si_conn_recv_cb(struct connection *conn)
 			break;
 		}
 
-		ret = conn->xprt->rcv_buf(conn, ic->buf, max);
+		ret = conn->mux->rcv_buf(cs, ic->buf, max);
 		if (ret <= 0)
 			break;
 
@@ -1203,9 +1215,12 @@ static void si_conn_recv_cb(struct connection *conn)
 		}
 
 		if ((ic->flags & CF_READ_DONTWAIT) || --read_poll <= 0) {
-			if (__conn_xprt_done_recv(conn))
-				si->flags |= SI_FL_WAIT_ROOM;
-			break;
+			/*
+			 * This used to be __conn_xprt_done_recv()
+			 * This was changed to accomodate with the mux code,
+			 * but we may have lost a worthwhile optimization.
+			 */
+			__cs_stop_recv(cs);
 		}
 
 		/* if too many bytes were missing from last read, it means that
@@ -1271,7 +1286,7 @@ static void si_conn_recv_cb(struct connection *conn)
 	if (conn->flags & CO_FL_ERROR)
 		return;
 
-	if (conn_xprt_read0_pending(conn))
+	if (cs->flags & CS_FL_EOS)
 		/* connection closed */
 		goto out_shutdown_r;
 
@@ -1291,9 +1306,10 @@ static void si_conn_recv_cb(struct connection *conn)
  * from the buffer to the connection. It iterates over the transport layer's
  * snd_buf function.
  */
-static void si_conn_send_cb(struct connection *conn)
+static void si_cs_send_cb(struct conn_stream *cs)
 {
-	struct stream_interface *si = conn->owner;
+	struct connection *conn = cs->conn;
+	struct stream_interface *si = cs->data;
 
 	if (conn->flags & CO_FL_ERROR)
 		return;
@@ -1307,7 +1323,7 @@ static void si_conn_send_cb(struct connection *conn)
 		return;
 
 	/* OK there are data waiting to be sent */
-	si_conn_send(conn);
+	si_cs_send(cs);
 
 	/* OK all done */
 	return;
@@ -1320,7 +1336,7 @@ static void si_conn_send_cb(struct connection *conn)
  */
 void stream_sock_read0(struct stream_interface *si)
 {
-	struct connection *conn = __objt_conn(si->end);
+	struct conn_stream *cs = __objt_cs(si->end);
 	struct channel *ic = si_ic(si);
 	struct channel *oc = si_oc(si);
 
@@ -1340,17 +1356,17 @@ void stream_sock_read0(struct stream_interface *si)
 	if (si->flags & SI_FL_NOHALF) {
 		/* we want to immediately forward this close to the write side */
 		/* force flag on ssl to keep stream in cache */
-		conn_xprt_shutw_hard(conn);
+		cs_shutw_hard(cs);
 		goto do_close;
 	}
 
 	/* otherwise that's just a normal read shutdown */
-	__conn_xprt_stop_recv(conn);
+	__cs_stop_recv(cs);
 	return;
 
  do_close:
 	/* OK we completely close the socket here just as if we went through si_shut[rw]() */
-	conn_full_close(conn);
+	conn_full_close(cs->conn);
 
 	ic->flags &= ~CF_SHUTR_NOW;
 	ic->flags |= CF_SHUTR;