diff --git a/modules/juce_audio_formats/codecs/juce_FlacAudioFormat.cpp b/modules/juce_audio_formats/codecs/juce_FlacAudioFormat.cpp
index da65398737..8e389f52ce 100644
--- a/modules/juce_audio_formats/codecs/juce_FlacAudioFormat.cpp
+++ b/modules/juce_audio_formats/codecs/juce_FlacAudioFormat.cpp
@@ -274,7 +274,8 @@ public:
         if (! remainingSamples.isEmpty())
             for (int i = numDestChannels; --i >= 0;)
                 if (destSamples[i] != nullptr)
-                    zeromem (destSamples[i] + startOffsetInDestBuffer, (size_t) remainingSamples.getLength() * sizeof (int));
+                    zeromem (destSamples[i] + startOffsetInDestBuffer + (remainingSamples.getStart() - startSampleInFile),
+                             (size_t) remainingSamples.getLength() * sizeof (int));
 
         return true;
     }
diff --git a/modules/juce_audio_formats/codecs/juce_OggVorbisAudioFormat.cpp b/modules/juce_audio_formats/codecs/juce_OggVorbisAudioFormat.cpp
index d1e0efdb60..b47c4a4d39 100644
--- a/modules/juce_audio_formats/codecs/juce_OggVorbisAudioFormat.cpp
+++ b/modules/juce_audio_formats/codecs/juce_OggVorbisAudioFormat.cpp
@@ -216,7 +216,8 @@ public:
         if (! remainingSamples.isEmpty())
             for (int i = numDestChannels; --i >= 0;)
                 if (destSamples[i] != nullptr)
-                    zeromem (destSamples[i] + startOffsetInDestBuffer, (size_t) remainingSamples.getLength() * sizeof (int));
+                    zeromem (destSamples[i] + startOffsetInDestBuffer + (remainingSamples.getStart() - startSampleInFile),
+                             (size_t) remainingSamples.getLength() * sizeof (int));
 
         return true;
     }