diff --git a/libavcodec/mpegaudiodec_template.c b/libavcodec/mpegaudiodec_template.c
index 1cc5ac47f4..9081a3ca94 100644
--- a/libavcodec/mpegaudiodec_template.c
+++ b/libavcodec/mpegaudiodec_template.c
@@ -1686,7 +1686,7 @@ static int decode_frame(AVCodecContext * avctx, void *data, int *got_frame_ptr,
     if (!avctx->bit_rate)
         avctx->bit_rate = s->bit_rate;
 
-    if (s->frame_size <= 0 || s->frame_size > buf_size) {
+    if (s->frame_size <= 0) {
         av_log(avctx, AV_LOG_ERROR, "incomplete frame\n");
         return AVERROR_INVALIDDATA;
     } else if (s->frame_size < buf_size) {
diff --git a/libavformat/mov.c b/libavformat/mov.c
index 5ea6932801..47628165fd 100644
--- a/libavformat/mov.c
+++ b/libavformat/mov.c
@@ -1669,6 +1669,15 @@ static void mov_parse_stsd_audio(MOVContext *c, AVIOContext *pb,
                     ff_mov_get_lpcm_codec_id(st->codec->bits_per_coded_sample,
                                              flags);
         }
+        if (version == 0 || (version == 1 && sc->audio_cid != -2)) {
+            /* can't correctly handle variable sized packet as audio unit */
+            switch (st->codec->codec_id) {
+            case AV_CODEC_ID_MP2:
+            case AV_CODEC_ID_MP3:
+                st->need_parsing = AVSTREAM_PARSE_FULL;
+                break;
+            }
+        }
     }
 
     switch (st->codec->codec_id) {
@@ -1889,7 +1898,6 @@ static int mov_finalize_stsd_codec(MOVContext *c, AVIOContext *pb,
     case AV_CODEC_ID_MP3:
         /* force type after stsd for m1a hdlr */
         st->codec->codec_type = AVMEDIA_TYPE_AUDIO;
-        st->need_parsing      = AVSTREAM_PARSE_FULL;
         break;
     case AV_CODEC_ID_GSM:
     case AV_CODEC_ID_ADPCM_MS:
diff --git a/tests/fate/mp3.mak b/tests/fate/mp3.mak
index 57ee08414b..a7b46c0969 100644
--- a/tests/fate/mp3.mak
+++ b/tests/fate/mp3.mak
@@ -1,6 +1,6 @@
 FATE_MP3 += fate-mp3-float-conf-compl
 fate-mp3-float-conf-compl: CMD = pcm -acodec mp3float -i $(TARGET_SAMPLES)/mp3-conformance/compl.bit
-fate-mp3-float-conf-compl: REF = $(SAMPLES)/mp3-conformance/compl.pcm
+fate-mp3-float-conf-compl: REF = $(SAMPLES)/mp3-conformance/compl_2.pcm
 
 FATE_MP3 += fate-mp3-float-conf-he_32khz
 fate-mp3-float-conf-he_32khz: CMD = pcm -acodec mp3float -i $(TARGET_SAMPLES)/mp3-conformance/he_32khz.bit -fs 343296