diff --git a/lib/media/streaming_engine.js b/lib/media/streaming_engine.js
index 45c8bb288..24bfc2e0f 100644
--- a/lib/media/streaming_engine.js
+++ b/lib/media/streaming_engine.js
@@ -1528,7 +1528,10 @@ shaka.media.StreamingEngine.prototype.handleStartup_ = function(
 
   goog.asserts.assert(
       mediaStates.every(function(ms) {
-        return ms.needPeriodIndex == currentPeriodIndex;
+        // It is possible for one stream (usually text) to buffer the whole
+        // Period and need the next one.
+        return ms.needPeriodIndex == currentPeriodIndex ||
+            ms.needPeriodIndex == currentPeriodIndex + 1;
       }),
       logPrefix + ' expected all MediaStates to need same Period');