diff --git a/src/mux_h1.c b/src/mux_h1.c
index 27b1cb674..c1eefe2b8 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -2491,7 +2491,11 @@ static void h1_detach(struct conn_stream *cs)
 		h1_release(h1c);
 	}
 	else {
-		h1c->conn->xprt->subscribe(h1c->conn, h1c->conn->xprt_ctx, SUB_RETRY_RECV, &h1c->wait_event);
+		/* If we have a new request, process it immediately */
+		if (unlikely(b_data(&h1c->conn)))
+			h1_process(h1c);
+		else
+			h1c->conn->xprt->subscribe(h1c->conn, h1c->conn->xprt_ctx, SUB_RETRY_RECV, &h1c->wait_event);
 		if (h1c->task) {
 			h1c->task->expire = TICK_ETERNITY;
 			if (b_data(&h1c->obuf)) {