diff --git a/include/types/connection.h b/include/types/connection.h
index 60036d6a1..2ed39f69c 100644
--- a/include/types/connection.h
+++ b/include/types/connection.h
@@ -327,6 +327,7 @@ struct mux_ops {
 	int (*subscribe)(struct conn_stream *cs, int event_type, void *param); /* Subscribe to events, such as "being able to send" */
 	int (*unsubscribe)(struct conn_stream *cs, int event_type, void *param); /* Unsubscribe to events */
 	int (*avail_streams)(struct connection *conn); /* Returns the number of streams still available for a connection */
+	void (*destroy)(struct connection *conn); /* Let the mux know one of its users left, so it may have to disappear */
 	unsigned int flags;                           /* some flags characterizing the mux's capabilities (MX_FL_*) */
 	char name[8];                                 /* mux layer name, zero-terminated */
 };
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 733cc1844..87b5cb1dc 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2478,7 +2478,6 @@ static int h2_wake(struct connection *conn)
 	return (h2_process(h2c));
 }
 
-
 /* Connection timeout management. The principle is that if there's no receipt
  * nor sending for a certain amount of time, the connection is closed. If the
  * MUX buffer still has lying data or is not allocatable, the connection is
@@ -2567,6 +2566,17 @@ static const struct conn_stream *h2_get_first_cs(const struct connection *conn)
 	return NULL;
 }
 
+/*
+ * Destroy the mux and the associated connection, if it is no longer used
+ */
+static void h2_destroy(struct connection *conn)
+{
+	struct h2c *h2c = conn->mux_ctx;
+
+	if (eb_is_empty(&h2c->streams_by_id))
+		h2_release(h2c->conn);
+}
+
 /*
  * Detach the stream from the connection and possibly release the connection.
  */
@@ -3800,6 +3810,7 @@ const struct mux_ops h2_ops = {
 	.attach = h2_attach,
 	.get_first_cs = h2_get_first_cs,
 	.detach = h2_detach,
+	.destroy = h2_destroy,
 	.avail_streams = h2_avail_streams,
 	.shutr = h2_shutr,
 	.shutw = h2_shutw,
diff --git a/src/mux_pt.c b/src/mux_pt.c
index d7ddcde88..a0f039775 100644
--- a/src/mux_pt.c
+++ b/src/mux_pt.c
@@ -149,6 +149,12 @@ static const struct conn_stream *mux_pt_get_first_cs(const struct connection *co
 	return cs;
 }
 
+/* Destroy the mux and the associated connection */
+static void mux_pt_destroy_meth(struct connection *conn)
+{
+	mux_pt_destroy(conn->mux_ctx);
+}
+
 /*
  * Detach the stream from the connection and possibly release the connection.
  */
@@ -269,6 +275,7 @@ const struct mux_ops mux_pt_ops = {
 	.get_first_cs = mux_pt_get_first_cs,
 	.detach = mux_pt_detach,
 	.avail_streams = mux_pt_avail_streams,
+	.destroy = mux_pt_destroy_meth,
 	.shutr = mux_pt_shutr,
 	.shutw = mux_pt_shutw,
 	.flags = MX_FL_NONE,