diff --git a/libavformat/movenc.c b/libavformat/movenc.c
index 3a9d015d0e..c326999327 100644
--- a/libavformat/movenc.c
+++ b/libavformat/movenc.c
@@ -72,7 +72,7 @@ static const AVOption options[] = {
     { "ism_lookahead", "Number of lookahead entries for ISM files", offsetof(MOVMuxContext, ism_lookahead), AV_OPT_TYPE_INT, {.i64 = 0}, 0, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM},
     { "brand",    "Override major brand", offsetof(MOVMuxContext, major_brand),   AV_OPT_TYPE_STRING, {.str = NULL}, .flags = AV_OPT_FLAG_ENCODING_PARAM },
     { "use_editlist", "use edit list", offsetof(MOVMuxContext, use_editlist), AV_OPT_TYPE_INT, {.i64 = -1}, -1, 1, AV_OPT_FLAG_ENCODING_PARAM},
-    { "fragment_index", "Fragment number of the next fragment", offsetof(MOVMuxContext, fragments), AV_OPT_TYPE_INT, {.i64 = 0}, 0, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM},
+    { "fragment_index", "Fragment number of the next fragment", offsetof(MOVMuxContext, fragments), AV_OPT_TYPE_INT, {.i64 = 1}, 1, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM},
     { NULL },
 };
 
@@ -3119,7 +3119,7 @@ static int mov_flush_fragment(AVFormatContext *s)
     if (!(mov->flags & FF_MOV_FLAG_FRAGMENT))
         return 0;
 
-    if (mov->fragments == 0) {
+    if (!mov->moov_written) {
         int64_t pos = avio_tell(s->pb);
         int ret;
         AVIOContext *moov_buf;
@@ -3148,7 +3148,7 @@ static int mov_flush_fragment(AVFormatContext *s)
             if (mov->flags & FF_MOV_FLAG_FASTSTART)
                 mov->reserved_moov_pos = avio_tell(s->pb);
             avio_flush(s->pb);
-            mov->fragments++;
+            mov->moov_written = 1;
             return 0;
         }
 
@@ -3159,7 +3159,7 @@ static int mov_flush_fragment(AVFormatContext *s)
         avio_write(s->pb, buf, buf_size);
         av_free(buf);
 
-        mov->fragments++;
+        mov->moov_written = 1;
         mov->mdat_size = 0;
         for (i = 0; i < mov->nb_streams; i++) {
             if (mov->tracks[i].entry)
@@ -3237,12 +3237,13 @@ static int mov_flush_fragment(AVFormatContext *s)
 static int mov_auto_flush_fragment(AVFormatContext *s)
 {
     MOVMuxContext *mov = s->priv_data;
+    int had_moov = mov->moov_written;
     int ret = mov_flush_fragment(s);
     if (ret < 0)
         return ret;
     // If using delay_moov, the first flush only wrote the moov,
     // not the actual moof+mdat pair, thus flush once again.
-    if (mov->fragments == 1 && mov->flags & FF_MOV_FLAG_DELAY_MOOV)
+    if (!had_moov && mov->flags & FF_MOV_FLAG_DELAY_MOOV)
         ret = mov_flush_fragment(s);
     return ret;
 }
@@ -3259,7 +3260,7 @@ int ff_mov_write_packet(AVFormatContext *s, AVPacket *pkt)
 
     if (mov->flags & FF_MOV_FLAG_FRAGMENT) {
         int ret;
-        if (mov->fragments > 0 || mov->flags & FF_MOV_FLAG_EMPTY_MOOV) {
+        if (mov->moov_written || mov->flags & FF_MOV_FLAG_EMPTY_MOOV) {
             if (!trk->mdat_buf) {
                 if ((ret = avio_open_dyn_buf(&trk->mdat_buf)) < 0)
                     return ret;
@@ -3391,7 +3392,7 @@ int ff_mov_write_packet(AVFormatContext *s, AVPacket *pkt)
             trk->frag_start   = pkt->dts;
             trk->start_dts    = 0;
             trk->frag_discont = 0;
-        } else if (pkt->dts && mov->fragments >= 1)
+        } else if (pkt->dts && mov->moov_written)
             av_log(s, AV_LOG_WARNING,
                    "Track %d starts with a nonzero dts %"PRId64", while the moov "
                    "already has been written. Set the delay_moov flag to handle "
@@ -3898,7 +3899,7 @@ static int mov_write_header(AVFormatContext *s)
     if (mov->flags & FF_MOV_FLAG_EMPTY_MOOV &&
         !(mov->flags & FF_MOV_FLAG_DELAY_MOOV)) {
         mov_write_moov_tag(pb, mov, s);
-        mov->fragments++;
+        mov->moov_written = 1;
         if (mov->flags & FF_MOV_FLAG_FASTSTART)
             mov->reserved_moov_pos = avio_tell(pb);
     }
diff --git a/libavformat/movenc.h b/libavformat/movenc.h
index 3ac53059b4..f64efad689 100644
--- a/libavformat/movenc.h
+++ b/libavformat/movenc.h
@@ -155,6 +155,7 @@ typedef struct MOVMuxContext {
     int iods_video_profile;
     int iods_audio_profile;
 
+    int moov_written;
     int fragments;
     int max_fragment_duration;
     int min_fragment_duration;