diff --git a/src/mux_h2.c b/src/mux_h2.c
index 8c73cce45..c4588eec5 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -3162,7 +3162,7 @@ static void h2_do_shutr(struct h2s *h2s)
 	struct h2c *h2c = h2s->h2c;
 	struct wait_event *sw = &h2s->wait_event;
 
-	if (h2s->st == H2_SS_HLOC || h2s->st == H2_SS_ERROR || h2s->st == H2_SS_CLOSED)
+	if (h2s->st == H2_SS_CLOSED)
 		goto done;
 
 	/* a connstream may require us to immediately kill the whole connection
@@ -3215,10 +3215,11 @@ static void h2_do_shutw(struct h2s *h2s)
 	struct h2c *h2c = h2s->h2c;
 	struct wait_event *sw = &h2s->wait_event;
 
-	if (h2s->st == H2_SS_HLOC || h2s->st == H2_SS_ERROR || h2s->st == H2_SS_CLOSED)
+	if (h2s->st == H2_SS_CLOSED)
 		goto done;
 
-	if (h2s->flags & H2_SF_HEADERS_SENT) {
+	if (h2s->st != H2_SS_HLOC && h2s->st != H2_SS_ERROR &&
+	    (h2s->flags & H2_SF_HEADERS_SENT)) {
 		/* we can cleanly close using an empty data frame only after headers */
 
 		if (!(h2s->flags & (H2_SF_ES_SENT|H2_SF_RST_SENT)) &&