diff --git a/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp b/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp
index b9be10278..74ad9d3d3 100644
--- a/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp
+++ b/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp
@@ -742,6 +742,11 @@ public:
    ~NoteTrackShifter() override {}
    Track &GetTrack() const override { return *mpTrack; }
 
+   HitTestResult HitTest( double ) override
+   {
+      return HitTestResult::Intervals;
+   }
+
 private:
    std::shared_ptr<NoteTrack> mpTrack;
 };
diff --git a/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp b/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp
index ebf9c8899..b00cb9c5b 100644
--- a/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp
+++ b/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp
@@ -1312,6 +1312,23 @@ public:
    ~WaveTrackShifter() override {}
    Track &GetTrack() const override { return *mpTrack; }
 
+   HitTestResult HitTest( double time ) override
+   {
+      auto pClip = mpTrack->GetClipAtTime( time );
+
+      if (!pClip)
+         return HitTestResult::Miss;
+
+      // Make a side-effect on our intervals
+      UnfixIntervals( [&](const auto &interval){
+         return
+            static_cast<WaveTrack::IntervalData*>(interval.Extra())
+               ->GetClip().get() == pClip;
+      } );
+      
+      return HitTestResult::Intervals;
+   }
+
 private:
    std::shared_ptr<WaveTrack> mpTrack;
 };
diff --git a/src/tracks/ui/TimeShiftHandle.cpp b/src/tracks/ui/TimeShiftHandle.cpp
index d7d34ebc0..a53324a5c 100644
--- a/src/tracks/ui/TimeShiftHandle.cpp
+++ b/src/tracks/ui/TimeShiftHandle.cpp
@@ -279,6 +279,11 @@ CoarseTrackShifter::CoarseTrackShifter( Track &track )
 
 CoarseTrackShifter::~CoarseTrackShifter() = default;
 
+auto CoarseTrackShifter::HitTest( double ) -> HitTestResult
+{
+   return HitTestResult::Track;
+}
+
 template<> auto MakeTrackShifter::Implementation() -> Function {
    return [](Track &track) {
       return std::make_unique<CoarseTrackShifter>(track);
@@ -494,29 +499,38 @@ UIHandle::Result TimeShiftHandle::Click
    mClipMoveState.capturedClip = NULL;
    mClipMoveState.capturedClipArray.clear();
 
-   bool ok = true;
    bool captureClips = false;
+   bool capturedAClip = false;
 
    auto pShifter = MakeTrackShifter::Call( *pTrack );
 
-   if (!event.ShiftDown())
-      pTrack->TypeSwitch(
-         [&](WaveTrack *wt) {
-            if (nullptr ==
-               (mClipMoveState.capturedClip = wt->GetClipAtX(event.m_x)))
-               ok = false;
-            else
-               captureClips = true;
-#ifdef USE_MIDI
-         },
-         [&](NoteTrack *) {
-            captureClips = true;
-#endif
-         }
-      );
+   if (!event.ShiftDown()) {
+      switch( pShifter->HitTest( clickTime ) ) {
+      case TrackShifter::HitTestResult::Miss:
+         return Cancelled;
+      case TrackShifter::HitTestResult::Intervals: {
+         captureClips = true;
+         if ( !pShifter->MovingIntervals().empty() ) {
+            capturedAClip = true;
 
-   if ( ! ok )
-      return Cancelled;
+            // There is still some code special to WaveTracks here that
+            // needs to go elsewhere
+            auto &interval = pShifter->MovingIntervals()[0];
+            auto pInfo =
+               dynamic_cast<WaveTrack::IntervalData*>(interval.Extra());
+            if ( pInfo )
+               mClipMoveState.capturedClip = pInfo->GetClip().get();
+         }
+         break;
+      }
+      case TrackShifter::HitTestResult::Track:
+      default:
+         break;
+      }
+   }
+   else {
+      // As in the default above: just do shifting of one whole track
+   }
 
    if ( captureClips ) {
       mClipMoveState.shifters[pTrack] = std::move( pShifter );
diff --git a/src/tracks/ui/TimeShiftHandle.h b/src/tracks/ui/TimeShiftHandle.h
index 4e4ff0acf..7aa942996 100644
--- a/src/tracks/ui/TimeShiftHandle.h
+++ b/src/tracks/ui/TimeShiftHandle.h
@@ -32,6 +32,17 @@ public:
    //! There is always an associated track
    virtual Track &GetTrack() const = 0;
 
+   //! Possibilities for HitTest on the clicked track
+   enum class HitTestResult {
+      Miss,      //!< Don't shift anything
+      Intervals, //<! May shift other tracks' intervals, if clicked in selection
+      Track      //<! Shift selected track only as a whole
+   };
+
+   //! Decide how shift behaves, based on the track that is clicked in
+   /*! If the return value is Intervals, then some intervals may be marked moving as a side effect */
+   virtual HitTestResult HitTest( double time ) = 0;
+
    using Intervals = std::vector<TrackInterval>;
 
    //! Return special intervals of the track that will not move
@@ -63,6 +74,8 @@ public:
    ~CoarseTrackShifter() override;
    Track &GetTrack() const override { return *mpTrack; }
 
+   HitTestResult HitTest( double ) override;
+
 private:
    std::shared_ptr<Track> mpTrack;
 };