diff --git a/lib/dash/dash_parser.js b/lib/dash/dash_parser.js
index 0652705fbf..d00dae49b4 100644
--- a/lib/dash/dash_parser.js
+++ b/lib/dash/dash_parser.js
@@ -592,7 +592,10 @@ shaka.dash.DashParser.prototype.parsePeriods_ = function(
       periodDuration = presentationDuration - start;
     }
 
-    if (periodDuration && givenDuration && periodDuration != givenDuration) {
+    var threshold =
+        shaka.util.ManifestParserUtils.GAP_OVERLAP_TOLERANCE_SECONDS;
+    if (periodDuration && givenDuration &&
+        Math.abs(periodDuration - givenDuration) > threshold) {
       shaka.log.warning('There is a gap/overlap between Periods', elem);
     }
     // Only use the @duration in the MPD if we can't calculate it.  We should
diff --git a/lib/util/stream_utils.js b/lib/util/stream_utils.js
index da9bd4ca6e..cc8e59bf00 100644
--- a/lib/util/stream_utils.js
+++ b/lib/util/stream_utils.js
@@ -573,9 +573,12 @@ shaka.util.StreamUtils.getFullMimeType = function(mimeType, opt_codecs) {
  * @return {number}
  */
 shaka.util.StreamUtils.findPeriodContainingTime = function(manifest, time) {
+  var threshold = shaka.util.ManifestParserUtils.GAP_OVERLAP_TOLERANCE_SECONDS;
   for (var i = manifest.periods.length - 1; i > 0; --i) {
     var period = manifest.periods[i];
-    if (time >= period.startTime)
+    // The last segment may end right before the end of the Period because of
+    // rounding issues.
+    if (time + threshold >= period.startTime)
       return i;
   }
   return 0;