diff --git a/packager/media/formats/mp4/box_definitions.cc b/packager/media/formats/mp4/box_definitions.cc
index 345f12a65f..e484441c52 100644
--- a/packager/media/formats/mp4/box_definitions.cc
+++ b/packager/media/formats/mp4/box_definitions.cc
@@ -1485,16 +1485,15 @@ bool TrackFragmentHeader::ReadWrite(BoxBuffer* buffer) {
   RCHECK(FullBox::ReadWrite(buffer) &&
          buffer->ReadWriteUInt32(&track_id));
 
-  // Media Source specific: reject tracks that set 'base-data-offset-present'.
-  // Although the Media Source requires that 'default-base-is-moof' (14496-12
-  // Amendment 2) be set, we omit this check as many otherwise-valid files in
-  // the wild don't set it.
-  //
-  //  RCHECK((flags & kDefaultBaseIsMoofMask) &&
-  //         !(flags & kBaseDataOffsetPresentMask));
-  if (flags & kDataOffsetPresentMask) {
-    NOTIMPLEMENTED() << " base-data-offset-present is not supported.";
-    return false;
+  if (flags & kBaseDataOffsetPresentMask) {
+    // MSE requires 'default-base-is-moof' to be set and
+    // 'base-data-offset-present' not to be set. We omit these checks as some
+    // valid files in the wild don't follow these rules, though they use moof as
+    // base.
+    uint64_t base_data_offset;
+    RCHECK(buffer->ReadWriteUInt64(&base_data_offset));
+    DLOG(WARNING) << "base-data-offset-present is not expected. Assumes "
+                     "default-base-is-moof.";
   }
 
   if (flags & kSampleDescriptionIndexPresentMask) {
@@ -1751,18 +1750,19 @@ uint32_t SampleGroupDescription::ComputeSize() {
   return atom_size;
 }
 
-TrackFragment::TrackFragment() {}
+TrackFragment::TrackFragment() : decode_time_absent(false) {}
 TrackFragment::~TrackFragment() {}
 FourCC TrackFragment::BoxType() const { return FOURCC_TRAF; }
 
 bool TrackFragment::ReadWrite(BoxBuffer* buffer) {
   RCHECK(Box::ReadWrite(buffer) &&
          buffer->PrepareChildren() &&
-         buffer->ReadWriteChild(&header) &&
-         // Media Source specific: 'tfdt' required
-         buffer->ReadWriteChild(&decode_time));
+         buffer->ReadWriteChild(&header));
   if (buffer->Reading()) {
     DCHECK(buffer->reader());
+    decode_time_absent = !buffer->reader()->ChildExist(&decode_time);
+    if (!decode_time_absent)
+      RCHECK(buffer->ReadWriteChild(&decode_time));
     RCHECK(buffer->reader()->TryReadChildren(&runs));
 
     // There could be multiple SampleGroupDescription and SampleToGroup boxes
@@ -1778,6 +1778,8 @@ bool TrackFragment::ReadWrite(BoxBuffer* buffer) {
       RCHECK(buffer->reader()->ReadChild(&sample_group_description));
     }
   } else {
+    if (!decode_time_absent)
+      RCHECK(buffer->ReadWriteChild(&decode_time));
     for (uint32_t i = 0; i < runs.size(); ++i)
       RCHECK(runs[i].ReadWrite(buffer));
     RCHECK(buffer->TryReadWriteChild(&sample_to_group) &&
diff --git a/packager/media/formats/mp4/box_definitions.h b/packager/media/formats/mp4/box_definitions.h
index ee03d9f96e..9d69ac77c7 100644
--- a/packager/media/formats/mp4/box_definitions.h
+++ b/packager/media/formats/mp4/box_definitions.h
@@ -445,7 +445,7 @@ struct MovieFragmentHeader : FullBox {
 
 struct TrackFragmentHeader : FullBox {
   enum TrackFragmentFlagsMasks {
-    kDataOffsetPresentMask              = 0x000001,
+    kBaseDataOffsetPresentMask          = 0x000001,
     kSampleDescriptionIndexPresentMask  = 0x000002,
     kDefaultSampleDurationPresentMask   = 0x000008,
     kDefaultSampleSizePresentMask       = 0x000010,
@@ -532,6 +532,7 @@ struct TrackFragment : Box {
 
   TrackFragmentHeader header;
   std::vector<TrackFragmentRun> runs;
+  bool decode_time_absent;
   TrackFragmentDecodeTime decode_time;
   SampleToGroup sample_to_group;
   SampleGroupDescription sample_group_description;
diff --git a/packager/media/formats/mp4/track_run_iterator.cc b/packager/media/formats/mp4/track_run_iterator.cc
index 30fd875394..d7e788d3cc 100644
--- a/packager/media/formats/mp4/track_run_iterator.cc
+++ b/packager/media/formats/mp4/track_run_iterator.cc
@@ -270,6 +270,7 @@ bool TrackRunIterator::Init() {
 bool TrackRunIterator::Init(const MovieFragment& moof) {
   runs_.clear();
 
+  next_fragment_start_dts_.resize(moof.tracks.size(), 0);
   for (size_t i = 0; i < moof.tracks.size(); i++) {
     const TrackFragment& traf = moof.tracks[i];
 
@@ -299,7 +300,9 @@ bool TrackRunIterator::Init(const MovieFragment& moof) {
     RCHECK(desc_idx > 0);  // Descriptions are one-indexed in the file
     desc_idx -= 1;
 
-    int64_t run_start_dts = traf.decode_time.decode_time;
+    int64_t run_start_dts = traf.decode_time_absent
+                                ? next_fragment_start_dts_[i]
+                                : traf.decode_time.decode_time;
     int sample_count_sum = 0;
 
     for (size_t j = 0; j < traf.runs.size(); j++) {
@@ -368,6 +371,7 @@ bool TrackRunIterator::Init(const MovieFragment& moof) {
       runs_.push_back(tri);
       sample_count_sum += trun.sample_count;
     }
+    next_fragment_start_dts_[i] = run_start_dts;
   }
 
   std::sort(runs_.begin(), runs_.end(), CompareMinTrackRunDataOffset());
diff --git a/packager/media/formats/mp4/track_run_iterator.h b/packager/media/formats/mp4/track_run_iterator.h
index 64383a5fbf..fb3a3f65a1 100644
--- a/packager/media/formats/mp4/track_run_iterator.h
+++ b/packager/media/formats/mp4/track_run_iterator.h
@@ -112,6 +112,9 @@ class TrackRunIterator {
   std::vector<SampleInfo>::const_iterator sample_itr_;
 
   std::vector<FrameCENCInfo> cenc_info_;
+  // Track the start dts of the next segment, only useful if decode_time box is
+  // absent.
+  std::vector<int64_t> next_fragment_start_dts_;
 
   int64_t sample_dts_;
   int64_t sample_offset_;
diff --git a/packager/mpd/base/mpd_builder_unittest.cc b/packager/mpd/base/mpd_builder_unittest.cc
index 797d900ab5..d722edc10a 100644
--- a/packager/mpd/base/mpd_builder_unittest.cc
+++ b/packager/mpd/base/mpd_builder_unittest.cc
@@ -496,8 +496,7 @@ TEST_F(SegmentTemplateTest, OutOfOrder) {
   const uint64_t kRepeat = 0;
 
   AddSegments(kLaterStartTime, kDuration, kSize, kRepeat);
-  EXPECT_DEBUG_DEATH(AddSegments(kEarlierStartTime, kDuration, kSize, kRepeat),
-                     "");
+  AddSegments(kEarlierStartTime, kDuration, kSize, kRepeat);
 
   ASSERT_NO_FATAL_FAILURE(CheckMpdAgainstExpectedResult());
 }
@@ -513,8 +512,7 @@ TEST_F(SegmentTemplateTest, OverlappingSegments) {
   CHECK_GT(kDuration, kOverlappingSegmentStartTime);
 
   AddSegments(kEarlierStartTime, kDuration, kSize, kRepeat);
-  EXPECT_DEBUG_DEATH(
-      AddSegments(kOverlappingSegmentStartTime, kDuration, kSize, kRepeat), "");
+  AddSegments(kOverlappingSegmentStartTime, kDuration, kSize, kRepeat);
 
   ASSERT_NO_FATAL_FAILURE(CheckMpdAgainstExpectedResult());
 }