diff --git a/include/haproxy/session.h b/include/haproxy/session.h
index 8ec1f7df5..6b1824aba 100644
--- a/include/haproxy/session.h
+++ b/include/haproxy/session.h
@@ -225,8 +225,12 @@ static inline int session_add_conn(struct session *sess, struct connection *conn
 	return 1;
 }
 
-/* Returns 0 if the session can keep the idle conn, -1 if it was destroyed. The
- * connection must be private.
+/* Check that session <sess> is able to keep idle connection <conn>. This must
+ * be called after insertion of a private connection into session unless
+ * connection is or will be soon active.
+ *
+ * Returns 0 if the connection is kept or is not attached to the session, else
+ * non-zero if the connection was explicitely removed from session.
  */
 static inline int session_check_idle_conn(struct session *sess, struct connection *conn)
 {
@@ -243,7 +247,6 @@ static inline int session_check_idle_conn(struct session *sess, struct connectio
 	if (sess->idle_conns >= sess->fe->max_out_conns) {
 		session_unown_conn(sess, conn);
 		conn->owner = NULL;
-		conn->mux->destroy(conn->ctx);
 		return -1;
 	}
 	else {
diff --git a/src/mux_fcgi.c b/src/mux_fcgi.c
index ce607422b..f91abf207 100644
--- a/src/mux_fcgi.c
+++ b/src/mux_fcgi.c
@@ -3738,7 +3738,7 @@ static void fcgi_detach(struct sedesc *sd)
 				 */
 				HA_ATOMIC_OR(&fconn->wait_event.tasklet->state, TASK_F_USR1);
 				if (session_check_idle_conn(fconn->conn->owner, fconn->conn) != 0) {
-					/* The connection is destroyed, let's leave */
+					fconn->conn->mux->destroy(fconn);
 					TRACE_DEVEL("outgoing connection killed", FCGI_EV_STRM_END|FCGI_EV_FCONN_ERR);
 					return;
 				}
diff --git a/src/mux_h1.c b/src/mux_h1.c
index 1e9c2b0de..a986483ef 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -1150,8 +1150,8 @@ static int h1s_finish_detach(struct h1s *h1s)
 			 */
 			HA_ATOMIC_OR(&h1c->wait_event.tasklet->state, TASK_F_USR1);
 			if (session_check_idle_conn(sess, h1c->conn)) {
-				/* The connection got destroyed, let's leave */
-				TRACE_DEVEL("outgoing connection killed", H1_EV_STRM_END|H1_EV_H1C_END);
+				TRACE_DEVEL("outgoing connection rejected", H1_EV_STRM_END|H1_EV_H1C_END, h1c->conn);
+				h1c->conn->mux->destroy(h1c);
 				goto released;
 			}
 		}
diff --git a/src/mux_h2.c b/src/mux_h2.c
index b893f5db2..de2533c05 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -5547,7 +5547,7 @@ static void h2_detach(struct sedesc *sd)
 					 */
 					HA_ATOMIC_OR(&h2c->wait_event.tasklet->state, TASK_F_USR1);
 					if (session_check_idle_conn(h2c->conn->owner, h2c->conn) != 0) {
-						/* At this point either the connection is destroyed, or it's been added to the server idle list, just stop */
+						h2c->conn->mux->destroy(h2c);
 						TRACE_DEVEL("leaving without reusable idle connection", H2_EV_STRM_END);
 						return;
 					}
diff --git a/src/mux_quic.c b/src/mux_quic.c
index 2faa3cc1c..093b71fe4 100644
--- a/src/mux_quic.c
+++ b/src/mux_quic.c
@@ -3784,24 +3784,24 @@ static void qmux_strm_detach(struct sedesc *sd)
 		if (conn->flags & CO_FL_PRIVATE) {
 			TRACE_DEVEL("handle private connection reuse", QMUX_EV_STRM_END, conn);
 
-			/* Add connection into session. If an error occured,
-			 * conn will be closed if idle, or insert will be
-			 * retried on next detach.
+			/* Ensure conn is attached into session. Most of the times
+			 * this is already done during connect so this is a no-op.
 			 */
 			if (!session_add_conn(sess, conn)) {
 				TRACE_ERROR("error during connection insert into session list", QMUX_EV_STRM_END, conn);
 				conn->owner = NULL;
+
+				/* Session insert failure. Close conn if idle,
+				 * else insert will be retry on next detach.
+				 */
 				if (!qcc->nb_sc)
 					goto release;
 			}
 
-			/* If conn is idle, check if session can keep it. Conn is freed if this is not the case.
-			 * TODO graceful shutdown should be preferable instead of plain mux->destroy().
-			 */
+			/* If conn is idle, check if session can keep it. Conn is closed if this is not the case. */
 			if (!qcc->nb_sc && session_check_idle_conn(sess, conn)) {
-				TRACE_DEVEL("idle conn rejected by session", QMUX_EV_STRM_END);
-				conn = NULL;
-				goto end;
+				TRACE_DEVEL("idle conn rejected by session", QMUX_EV_STRM_END, conn);
+				goto release;
 			}
 		}
 		else {
diff --git a/src/mux_spop.c b/src/mux_spop.c
index 622515b37..a9bc0aab8 100644
--- a/src/mux_spop.c
+++ b/src/mux_spop.c
@@ -2991,7 +2991,7 @@ static void spop_detach(struct sedesc *sd)
 				 */
 				HA_ATOMIC_OR(&spop_conn->wait_event.tasklet->state, TASK_F_USR1);
 				if (session_check_idle_conn(spop_conn->conn->owner, spop_conn->conn) != 0) {
-					/* At this point either the connection is destroyed, or it's been added to the server idle list, just stop */
+					spop_conn->conn->mux->destroy(spop_conn);
 					TRACE_DEVEL("leaving without reusable idle connection", SPOP_EV_STRM_END);
 					return;
 				}