diff --git a/include/proto/connection.h b/include/proto/connection.h
index fbb37904d..8ba4fc632 100644
--- a/include/proto/connection.h
+++ b/include/proto/connection.h
@@ -757,17 +757,17 @@ static inline const struct mux_ops *conn_find_best_mux(struct connection *conn,
 }
 
 /* finds the best mux for incoming connection <conn>, a proxy in and http mode
- * <mode>, and installs it on the connection for direction <dir> (MUX_INBOUND/
- * MUX_OUTBOUND). Returns < 0 on error.
+ * <mode>, and installs it on the connection for upper context <ctx>. Returns
+ * < 0 on error.
  */
-static inline int conn_install_best_mux(struct connection *conn, int mode, enum mux_dir dir)
+static inline int conn_install_best_mux(struct connection *conn, int mode, void *ctx)
 {
 	const struct mux_ops *mux_ops;
 
 	mux_ops = conn_find_best_mux(conn, mode);
 	if (!mux_ops)
 		return -1;
-	return conn_install_mux(conn, mux_ops, dir);
+	return conn_install_mux(conn, mux_ops, ctx);
 }
 
 #endif /* _PROTO_CONNECTION_H */
diff --git a/src/session.c b/src/session.c
index b0bf453ad..c68cec545 100644
--- a/src/session.c
+++ b/src/session.c
@@ -21,7 +21,6 @@
 #include <proto/connection.h>
 #include <proto/listener.h>
 #include <proto/log.h>
-#include <proto/mux_pt.h>
 #include <proto/proto_http.h>
 #include <proto/proxy.h>
 #include <proto/session.h>
@@ -407,7 +406,7 @@ static int conn_complete_session(struct connection *conn)
 		goto fail;
 
 	session_count_new(sess);
-	if (conn_install_mux(conn, &mux_pt_ops, NULL) < 0)
+	if (conn_install_best_mux(conn, sess->fe->mode == PR_MODE_HTTP, NULL) < 0)
 		goto fail;
 
 	/* the embryonic session's task is not needed anymore */