diff --git a/library/src/main/java/com/google/android/exoplayer/dash/DashChunkSource.java b/library/src/main/java/com/google/android/exoplayer/dash/DashChunkSource.java
index 8bf7199da8..76b40483d8 100644
--- a/library/src/main/java/com/google/android/exoplayer/dash/DashChunkSource.java
+++ b/library/src/main/java/com/google/android/exoplayer/dash/DashChunkSource.java
@@ -309,10 +309,26 @@ public class DashChunkSource implements ChunkSource {
         RepresentationHolder representationHolder =
             representationHolders.get(representation.format.id);
         DashSegmentIndex oldIndex = representationHolder.segmentIndex;
+        int oldIndexLastSegmentNum = oldIndex.getLastSegmentNum();
+        long oldIndexEndTimeUs = oldIndex.getTimeUs(oldIndexLastSegmentNum)
+            + oldIndex.getDurationUs(oldIndexLastSegmentNum);
         DashSegmentIndex newIndex = representation.getIndex();
-        int newFirstSegmentNum = newIndex.getFirstSegmentNum();
-        int segmentNumShift = oldIndex.getSegmentNum(newIndex.getTimeUs(newFirstSegmentNum))
-            - newFirstSegmentNum;
+        int newIndexFirstSegmentNum = newIndex.getFirstSegmentNum();
+        long newIndexStartTimeUs = newIndex.getTimeUs(newIndexFirstSegmentNum);
+        if (oldIndexEndTimeUs < newIndexStartTimeUs) {
+          // There's a gap between the old manifest and the new one which means we've slipped behind
+          // the live window and can't proceed.
+          fatalError = new BehindLiveWindowException();
+          return;
+        }
+        int segmentNumShift;
+        if (oldIndexEndTimeUs == newIndexStartTimeUs) {
+          // The new manifest continues where the old one ended, with no overlap.
+          segmentNumShift = oldIndex.getLastSegmentNum() + 1 - newIndexFirstSegmentNum;
+        } else {
+          // The new manifest overlaps with the old one.
+          segmentNumShift = oldIndex.getSegmentNum(newIndexStartTimeUs) - newIndexFirstSegmentNum;
+        }
         representationHolder.segmentNumShift += segmentNumShift;
         representationHolder.segmentIndex = newIndex;
       }
diff --git a/library/src/main/java/com/google/android/exoplayer/smoothstreaming/SmoothStreamingChunkSource.java b/library/src/main/java/com/google/android/exoplayer/smoothstreaming/SmoothStreamingChunkSource.java
index c7a3f2e517..77b187d464 100644
--- a/library/src/main/java/com/google/android/exoplayer/smoothstreaming/SmoothStreamingChunkSource.java
+++ b/library/src/main/java/com/google/android/exoplayer/smoothstreaming/SmoothStreamingChunkSource.java
@@ -217,11 +217,22 @@ public class SmoothStreamingChunkSource implements ChunkSource {
     SmoothStreamingManifest newManifest = manifestFetcher.getManifest();
     if (currentManifest != newManifest && newManifest != null) {
       StreamElement currentElement = getElement(currentManifest);
+      int currentElementChunkCount = currentElement.chunkCount;
       StreamElement newElement = getElement(newManifest);
-      if (newElement.chunkCount == 0) {
-        currentManifestChunkOffset += currentElement.chunkCount;
-      } else if (currentElement.chunkCount > 0) {
-        currentManifestChunkOffset += currentElement.getChunkIndex(newElement.getStartTimeUs(0));
+      if (currentElementChunkCount == 0 || newElement.chunkCount == 0) {
+        // There's no overlap between the old and new elements because at least one is empty.
+        currentManifestChunkOffset += currentElementChunkCount;
+      } else {
+        long currentElementEndTimeUs = currentElement.getStartTimeUs(currentElementChunkCount - 1)
+            + currentElement.getChunkDurationUs(currentElementChunkCount - 1);
+        long newElementStartTimeUs = newElement.getStartTimeUs(0);
+        if (currentElementEndTimeUs <= newElementStartTimeUs) {
+          // There's no overlap between the old and new elements.
+          currentManifestChunkOffset += currentElementChunkCount;
+        } else {
+          // The new element overlaps with the old one.
+          currentManifestChunkOffset += currentElement.getChunkIndex(newElementStartTimeUs);
+        }
       }
       currentManifest = newManifest;
       finishedCurrentManifest = false;