diff --git a/src/backend.c b/src/backend.c
index f7e5dbd..a52eacc 100644
--- a/src/backend.c
+++ b/src/backend.c
@@ -1189,8 +1189,7 @@
 		else
 			return SF_ERR_INTERNAL;  /* how did we get there ? */
 
-		/* XXX: Pick the right mux, when we finally have one */
-		conn_install_mux(srv_conn, &mux_pt_ops, srv_cs);
+		conn_install_best_mux(srv_conn, s->be->mode == PR_MODE_HTTP, srv_cs);
 
 		/* process the case where the server requires the PROXY protocol to be sent */
 		srv_conn->send_proxy_ofs = 0;