diff --git a/src/backend.c b/src/backend.c
index 9937a7f9f..c1f0ab213 100644
--- a/src/backend.c
+++ b/src/backend.c
@@ -2175,7 +2175,6 @@ int connect_server(struct stream *s)
 			return SF_ERR_INTERNAL;
 		}
 	}
-	conn_xprt_start(srv_conn);
 
 	/* We have to defer the mux initialization until after si_connect()
 	 * has been called, as we need the xprt to have been properly
@@ -2212,6 +2211,14 @@ int connect_server(struct stream *s)
 		}
 	}
 
+	/*
+	 * Now that the mux may have been created, we can start the xprt.
+	 * We had to wait until then, because the xprt may behave differently
+	 * depending on if a mux already exists, and it can receive data
+	 * from the stream, or not.
+	 */
+	conn_xprt_start(srv_conn);
+
 #if defined(HAVE_SSL_0RTT)
 	/* The flags change below deserve some explanation: when we want to
 	 * use early data, we first want to make sure that a mux is installed