diff --git a/src/mux_h2.c b/src/mux_h2.c
index 71660f8..c6e15ec 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2250,6 +2250,7 @@
 static int h2_wake(struct connection *conn)
 {
 	struct h2c *h2c = conn->mux_ctx;
+	struct session *sess = conn->owner;
 
 	if (h2c->dbuf->i && !(h2c->flags & H2_CF_DEM_BLOCK_ANY)) {
 		h2_process_demux(h2c);
@@ -2261,6 +2262,18 @@
 			h2c->flags &= ~H2_CF_DEM_DFULL;
 	}
 
+	if (sess && unlikely(sess->fe->state == PR_STSTOPPED)) {
+		/* frontend is stopping, reload likely in progress, let's try
+		 * to announce a graceful shutdown if not yet done. We don't
+		 * care if it fails, it will be tried again later.
+		 */
+		if (!(h2c->flags & (H2_CF_GOAWAY_SENT|H2_CF_GOAWAY_FAILED))) {
+			if (h2c->last_sid < 0)
+				h2c->last_sid = (1U << 31) - 1;
+			h2c_send_goaway_error(h2c, NULL);
+		}
+	}
+
 	/*
 	 * If we received early data, try to wake any stream, just in case
 	 * at least one of them was waiting for the handshake