diff --git a/include/haproxy/connection-t.h b/include/haproxy/connection-t.h
index 77e31eb46..ca7819616 100644
--- a/include/haproxy/connection-t.h
+++ b/include/haproxy/connection-t.h
@@ -41,6 +41,7 @@
 /* referenced below */
 struct connection;
 struct conn_stream;
+struct cs_endpoint;
 struct cs_info;
 struct buffer;
 struct proxy;
@@ -394,9 +395,9 @@ struct mux_ops {
 	void (*shutr)(struct conn_stream *cs, enum co_shr_mode);     /* shutr function */
 	void (*shutw)(struct conn_stream *cs, enum co_shw_mode);     /* shutw function */
 
-	int (*attach)(struct connection *conn, struct conn_stream *, struct session *sess); /* attach a conn_stream to an outgoing connection */
+	int (*attach)(struct connection *conn, struct cs_endpoint *, struct session *sess); /* attach a conn_stream to an outgoing connection */
 	struct conn_stream *(*get_first_cs)(const struct connection *); /* retrieves any valid conn_stream from this connection */
-	void (*detach)(struct conn_stream *); /* Detach a conn_stream from an outgoing connection, when the request is done */
+	void (*detach)(struct cs_endpoint *); /* Detach a conn_stream from an outgoing connection, when the request is done */
 	int (*show_fd)(struct buffer *, struct connection *); /* append some data about connection into chunk for "show fd"; returns non-zero if suspicious */
 	int (*subscribe)(struct conn_stream *cs, int event_type,  struct wait_event *es); /* Subscribe <es> to events, such as "being able to send" */
 	int (*unsubscribe)(struct conn_stream *cs, int event_type,  struct wait_event *es); /* Unsubscribe <es> from events */
diff --git a/src/backend.c b/src/backend.c
index 3b0e231c2..4a3a76426 100644
--- a/src/backend.c
+++ b/src/backend.c
@@ -1574,7 +1574,7 @@ static int connect_server(struct stream *s)
 			}
 
 			if (avail >= 1) {
-				if (srv_conn->mux->attach(srv_conn, s->csb, s->sess) == -1) {
+				if (srv_conn->mux->attach(srv_conn, s->csb->endp, s->sess) == -1) {
 					srv_conn = NULL;
 					if (cs_reset_endp(s->csb) < 0)
 						return SF_ERR_INTERNAL;
diff --git a/src/conn_stream.c b/src/conn_stream.c
index 5fda0d893..819f2cb4a 100644
--- a/src/conn_stream.c
+++ b/src/conn_stream.c
@@ -363,15 +363,16 @@ static void cs_detach_endp(struct conn_stream **csp)
 
 	if (cs->endp->flags & CS_EP_T_MUX) {
 		struct connection *conn = __cs_conn(cs);
+		struct cs_endpoint *endp = cs->endp;
 
 		if (conn->mux) {
 			/* TODO: handle unsubscribe for healthchecks too */
 			if (cs->wait_event.events != 0)
 				conn->mux->unsubscribe(cs, cs->wait_event.events, &cs->wait_event);
-			cs->endp->flags |= CS_EP_ORPHAN;
-			cs->endp->cs = NULL;
-			conn->mux->detach(cs);
+			endp->flags |= CS_EP_ORPHAN;
+			endp->cs = NULL;
 			cs->endp = NULL;
+			conn->mux->detach(endp);
 		}
 		else {
 			/* It's too early to have a mux, let's just destroy
diff --git a/src/mux_fcgi.c b/src/mux_fcgi.c
index 023c6529a..77eb457e3 100644
--- a/src/mux_fcgi.c
+++ b/src/mux_fcgi.c
@@ -3521,13 +3521,13 @@ static size_t fcgi_strm_parse_response(struct fcgi_strm *fstrm, struct buffer *b
  * Attach a new stream to a connection
  * (Used for outgoing connections)
  */
-static int fcgi_attach(struct connection *conn, struct conn_stream *cs, struct session *sess)
+static int fcgi_attach(struct connection *conn, struct cs_endpoint *endp, struct session *sess)
 {
 	struct fcgi_strm *fstrm;
 	struct fcgi_conn *fconn = conn->ctx;
 
 	TRACE_ENTER(FCGI_EV_FSTRM_NEW, conn);
-	fstrm = fcgi_conn_stream_new(fconn, cs, sess);
+	fstrm = fcgi_conn_stream_new(fconn, endp->cs, sess);
 	if (!fstrm)
 		goto err;
 
@@ -3581,9 +3581,9 @@ static void fcgi_destroy(void *ctx)
 /*
  * Detach the stream from the connection and possibly release the connection.
  */
-static void fcgi_detach(struct conn_stream *cs)
+static void fcgi_detach(struct cs_endpoint *endp)
 {
-	struct fcgi_strm *fstrm = __cs_mux(cs);
+	struct fcgi_strm *fstrm = endp->target;
 	struct fcgi_conn *fconn;
 	struct session *sess;
 
diff --git a/src/mux_h1.c b/src/mux_h1.c
index e74e0fb18..e41e6ef4c 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -3303,7 +3303,7 @@ struct task *h1_timeout_task(struct task *t, void *context, unsigned int state)
  * Attach a new stream to a connection
  * (Used for outgoing connections)
  */
-static int h1_attach(struct connection *conn, struct conn_stream *cs, struct session *sess)
+static int h1_attach(struct connection *conn, struct cs_endpoint *endp, struct session *sess)
 {
 	struct h1c *h1c = conn->ctx;
 	struct h1s *h1s;
@@ -3314,7 +3314,7 @@ static int h1_attach(struct connection *conn, struct conn_stream *cs, struct ses
 		goto err;
 	}
 
-	h1s = h1c_bck_stream_new(h1c, cs, sess);
+	h1s = h1c_bck_stream_new(h1c, endp->cs, sess);
 	if (h1s == NULL) {
 		TRACE_ERROR("h1s creation failure", H1_EV_STRM_NEW|H1_EV_STRM_END|H1_EV_STRM_ERR, conn);
 		goto err;
@@ -3357,9 +3357,9 @@ static void h1_destroy(void *ctx)
 /*
  * Detach the stream from the connection and possibly release the connection.
  */
-static void h1_detach(struct conn_stream *cs)
+static void h1_detach(struct cs_endpoint *endp)
 {
-	struct h1s *h1s = __cs_mux(cs);
+	struct h1s *h1s = endp->target;
 	struct h1c *h1c;
 	struct session *sess;
 	int is_not_first;
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 72d0b9f0e..6cb2334ba 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -4289,13 +4289,13 @@ do_leave:
  * Attach a new stream to a connection
  * (Used for outgoing connections)
  */
-static int h2_attach(struct connection *conn, struct conn_stream *cs, struct session *sess)
+static int h2_attach(struct connection *conn, struct cs_endpoint *endp, struct session *sess)
 {
 	struct h2s *h2s;
 	struct h2c *h2c = conn->ctx;
 
 	TRACE_ENTER(H2_EV_H2S_NEW, conn);
-	h2s = h2c_bck_stream_new(h2c, cs, sess);
+	h2s = h2c_bck_stream_new(h2c, endp->cs, sess);
 	if (!h2s) {
 		TRACE_DEVEL("leaving on stream creation failure", H2_EV_H2S_NEW|H2_EV_H2S_ERR, conn);
 		return -1;
@@ -4368,9 +4368,9 @@ static void h2_destroy(void *ctx)
 /*
  * Detach the stream from the connection and possibly release the connection.
  */
-static void h2_detach(struct conn_stream *cs)
+static void h2_detach(struct cs_endpoint *endp)
 {
-	struct h2s *h2s = __cs_mux(cs);
+	struct h2s *h2s = endp->target;
 	struct h2c *h2c;
 	struct session *sess;
 
diff --git a/src/mux_pt.c b/src/mux_pt.c
index 4638c7133..fa92ed6aa 100644
--- a/src/mux_pt.c
+++ b/src/mux_pt.c
@@ -373,19 +373,19 @@ static int mux_pt_wake(struct connection *conn)
  * Attach a new stream to a connection
  * (Used for outgoing connections)
  */
-static int mux_pt_attach(struct connection *conn, struct conn_stream *cs, struct session *sess)
+static int mux_pt_attach(struct connection *conn, struct cs_endpoint *endp, struct session *sess)
 {
 	struct mux_pt_ctx *ctx = conn->ctx;
 
 	TRACE_ENTER(PT_EV_STRM_NEW, conn);
 	if (ctx->wait_event.events)
 		conn->xprt->unsubscribe(ctx->conn, conn->xprt_ctx, SUB_RETRY_RECV, &ctx->wait_event);
-	if (cs_attach_mux(cs, ctx, conn) < 0)
+	if (cs_attach_mux(endp->cs, ctx, conn) < 0)
 		return -1;
-	ctx->endp = cs->endp;
+	ctx->endp = endp;
 	ctx->endp->flags |= CS_EP_RCV_MORE;
 
-	TRACE_LEAVE(PT_EV_STRM_NEW, conn, cs);
+	TRACE_LEAVE(PT_EV_STRM_NEW, conn, endp->cs);
 	return 0;
 }
 
@@ -417,12 +417,12 @@ static void mux_pt_destroy_meth(void *ctx)
 /*
  * Detach the stream from the connection and possibly release the connection.
  */
-static void mux_pt_detach(struct conn_stream *cs)
+static void mux_pt_detach(struct cs_endpoint *endp)
 {
-	struct connection *conn = __cs_conn(cs);
+	struct connection *conn = endp->ctx;
 	struct mux_pt_ctx *ctx;
 
-	TRACE_ENTER(PT_EV_STRM_END, conn, cs);
+	TRACE_ENTER(PT_EV_STRM_END, conn, endp->cs);
 
 	ctx = conn->ctx;
 
@@ -432,7 +432,7 @@ static void mux_pt_detach(struct conn_stream *cs)
 		conn->xprt->subscribe(conn, conn->xprt_ctx, SUB_RETRY_RECV, &ctx->wait_event);
 	} else {
 		/* There's no session attached to that connection, destroy it */
-		TRACE_DEVEL("killing dead connection", PT_EV_STRM_END, conn, cs);
+		TRACE_DEVEL("killing dead connection", PT_EV_STRM_END, conn, endp->cs);
 		mux_pt_destroy(ctx);
 	}
 
diff --git a/src/mux_quic.c b/src/mux_quic.c
index f03b651ee..8c9c051e0 100644
--- a/src/mux_quic.c
+++ b/src/mux_quic.c
@@ -1220,9 +1220,9 @@ static void qc_destroy(void *ctx)
 	TRACE_LEAVE(QMUX_EV_QCC_END);
 }
 
-static void qc_detach(struct conn_stream *cs)
+static void qc_detach(struct cs_endpoint *endp)
 {
-	struct qcs *qcs = __cs_mux(cs);
+	struct qcs *qcs = __cs_mux(endp->cs);
 	struct qcc *qcc = qcs->qcc;
 
 	TRACE_ENTER(QMUX_EV_STRM_END, qcc->conn, qcs);