diff --git a/lib/dash/dash_parser.js b/lib/dash/dash_parser.js
index c6898e75cc..6e88ddca35 100644
--- a/lib/dash/dash_parser.js
+++ b/lib/dash/dash_parser.js
@@ -513,6 +513,11 @@ shaka.dash.DashParser = class {
         }
         presentationTimeline.setClockOffset(offset);
       }
+
+      // This is the first point where we have a meaningful presentation start
+      // time, and we need to tell PresentationTimeline that so that it can
+      // maintain consistency from here on.
+      presentationTimeline.lockStartTime();
     } else {
       // Just update the variants and text streams, which may change as periods
       // are added or removed.
diff --git a/lib/hls/hls_parser.js b/lib/hls/hls_parser.js
index bb501da250..787eaeb2f0 100644
--- a/lib/hls/hls_parser.js
+++ b/lib/hls/hls_parser.js
@@ -740,8 +740,14 @@ shaka.hls.HlsParser = class {
     for (const stream of streamsToNotify) {
       this.segmentsToNotifyByStream_.push(stream.segmentIndex.references);
     }
+
     this.notifySegments_();
 
+    // This is the first point where we have a meaningful presentation start
+    // time, and we need to tell PresentationTimeline that so that it can
+    // maintain consistency from here on.
+    this.presentationTimeline_.lockStartTime();
+
     // This asserts that the live edge is being calculated from segment times.
     // For VOD and event streams, this check should still pass.
     goog.asserts.assert(
@@ -1859,8 +1865,6 @@ shaka.hls.HlsParser = class {
       /* presentationStartTime= */ null, /* delay= */ 0);
       this.presentationTimeline_.setStatic(true);
     }
-
-    this.notifySegments_();
   }
 
   /**
diff --git a/lib/media/presentation_timeline.js b/lib/media/presentation_timeline.js
index ba3ea3ec54..0a18b41405 100644
--- a/lib/media/presentation_timeline.js
+++ b/lib/media/presentation_timeline.js
@@ -93,6 +93,9 @@ shaka.media.PresentationTimeline = class {
      * @private {number}
      */
     this.availabilityTimeOffset_ = 0;
+
+    /** @private {boolean} */
+    this.startTimeLocked_ = false;
   }
 
 
@@ -229,7 +232,8 @@ shaka.media.PresentationTimeline = class {
     this.maxSegmentEndTime_ =
         Math.max(this.maxSegmentEndTime_, lastReferenceEndTime);
 
-    if (this.presentationStartTime_ != null && this.autoCorrectDrift_) {
+    if (this.presentationStartTime_ != null && this.autoCorrectDrift_ &&
+        !this.startTimeLocked_) {
       // Since we have explicit segment end times, calculate a presentation
       // start based on them.  This start time accounts for drift.
       // Date.now() is in milliseconds, from which we compute "now" in seconds.
@@ -243,6 +247,25 @@ shaka.media.PresentationTimeline = class {
   }
 
 
+  /**
+   * Lock the presentation timeline's start time.  After this is called, no
+   * further adjustments to presentationStartTime_ will be permitted.
+   *
+   * This should be called after all Periods have been parsed, and all calls to
+   * notifySegments() from the initial manifest parse have been made.
+   *
+   * Without this, we can get assertion failures in SegmentIndex for certain
+   * DAI content.  If DAI adds ad segments to the manifest faster than
+   * real-time, adjustments to presentationStartTime_ can cause availability
+   * windows to jump around on updates.
+   *
+   * @export
+   */
+  lockStartTime() {
+    this.startTimeLocked_ = true;
+  }
+
+
   /**
    * Gives PresentationTimeline a Stream's minimum segment start time.
    *