diff --git a/libavcodec/h264_parser.c b/libavcodec/h264_parser.c
index 27fba4b628..ad134b3f82 100644
--- a/libavcodec/h264_parser.c
+++ b/libavcodec/h264_parser.c
@@ -251,6 +251,12 @@ static int h264_parse(AVCodecParserContext *s,
         h->got_first = 1;
         if (avctx->extradata_size) {
             h->s.avctx = avctx;
+            // must be done like in decoder, otherwise opening the parser,
+            // letting it create extradata and then closing and opening again
+            // will cause has_b_frames to be always set.
+            // Note that estimate_timings_from_pts does exactly this.
+            if (!avctx->has_b_frames)
+                h->s.low_delay = 1;
             ff_h264_decode_extradata(h);
         }
     }