diff --git a/src/h1_htx.c b/src/h1_htx.c
index 3d74a4c99..61a60eeb5 100644
--- a/src/h1_htx.c
+++ b/src/h1_htx.c
@@ -878,8 +878,14 @@ int h1_parse_msg_tlrs(struct h1m *h1m, struct htx *dsthtx,
 	struct h1m tlr_h1m;
 	int ret = 0;
 
-	if (!max || !b_data(srcbuf))
+	if (b_data(srcbuf) == ofs) {
+		/* Nothing to parse */
 		goto end;
+	}
+	if (!max) {
+		/* No more room */
+		goto output_full;
+	}
 
 	/* Realing input buffer if necessary */
 	if (b_peek(srcbuf, ofs) > b_tail(srcbuf))
diff --git a/src/mux_h1.c b/src/mux_h1.c
index cd5f3fb73..79fdb553a 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -1709,7 +1709,7 @@ static size_t h1_handle_trailers(struct h1s *h1s, struct h1m *h1m, struct htx *h
 			TRACE_ERROR("parsing error, reject H1 message", H1_EV_RX_DATA|H1_EV_RX_TLRS|H1_EV_H1S_ERR, h1s->h1c->conn, h1s);
 			h1_capture_bad_message(h1s->h1c, h1s, h1m, buf);
 		}
-		else if (ret == -2 || b_data(buf) != *ofs) {
+		else if (ret == -2) {
 			TRACE_STATE("RX path congested, waiting for more space", H1_EV_RX_DATA|H1_EV_RX_TLRS|H1_EV_H1S_BLK, h1s->h1c->conn, h1s);
 			h1s->flags |= H1S_F_RX_CONGESTED;
 		}