diff --git a/src/mux_h2.c b/src/mux_h2.c
index eb773a2..f3fb284 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2915,7 +2915,7 @@
 	/* We're not full anymore, so we can wake any task that are waiting
 	 * for us.
 	 */
-	if (!(h2c->flags & (H2_CF_MUX_MFULL | H2_CF_DEM_MROOM))) {
+	if (!(h2c->flags & (H2_CF_MUX_MFULL | H2_CF_DEM_MROOM)) && h2c->st0 >= H2_CS_FRAME_H) {
 		struct h2s *h2s;
 
 		list_for_each_entry(h2s, &h2c->send_list, list) {