diff --git a/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp b/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp
index 09f4dc42f..b9be10278 100644
--- a/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp
+++ b/src/tracks/playabletrack/notetrack/ui/NoteTrackView.cpp
@@ -736,7 +736,9 @@ class NoteTrackShifter final : public TrackShifter {
 public:
    NoteTrackShifter( NoteTrack &track )
       : mpTrack{ track.SharedPointer<NoteTrack>() }
-   {}
+   {
+      InitIntervals();
+   }
    ~NoteTrackShifter() override {}
    Track &GetTrack() const override { return *mpTrack; }
 
diff --git a/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp b/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp
index 8739a62dd..ebf9c8899 100644
--- a/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp
+++ b/src/tracks/playabletrack/wavetrack/ui/WaveTrackView.cpp
@@ -1307,6 +1307,7 @@ public:
    WaveTrackShifter( WaveTrack &track )
       : mpTrack{ track.SharedPointer<WaveTrack>() }
    {
+      InitIntervals();
    }
    ~WaveTrackShifter() override {}
    Track &GetTrack() const override { return *mpTrack; }
diff --git a/src/tracks/ui/TimeShiftHandle.cpp b/src/tracks/ui/TimeShiftHandle.cpp
index acc58dbd9..d7d34ebc0 100644
--- a/src/tracks/ui/TimeShiftHandle.cpp
+++ b/src/tracks/ui/TimeShiftHandle.cpp
@@ -246,9 +246,36 @@ namespace
 
 TrackShifter::~TrackShifter() = default;
 
+void TrackShifter::UnfixIntervals(
+   std::function< bool( const TrackInterval& ) > pred )
+{
+   for ( auto iter = mFixed.begin(); iter != mFixed.end(); ) {
+      if ( pred( *iter) ) {
+         mMoving.push_back( std::move( *iter ) );
+         iter = mFixed.erase( iter );
+      }
+      else
+         ++iter;
+   }
+}
+
+void TrackShifter::UnfixAll()
+{
+   std::move( mFixed.begin(), mFixed.end(), std::back_inserter(mMoving) );
+   mFixed = Intervals{};
+}
+
+void TrackShifter::InitIntervals()
+{
+   mMoving.clear();
+   mFixed = GetTrack().GetIntervals();
+}
+
 CoarseTrackShifter::CoarseTrackShifter( Track &track )
    : mpTrack{ track.SharedPointer() }
-{}
+{
+   InitIntervals();
+}
 
 CoarseTrackShifter::~CoarseTrackShifter() = default;
 
diff --git a/src/tracks/ui/TimeShiftHandle.h b/src/tracks/ui/TimeShiftHandle.h
index 8e68354ba..4e4ff0acf 100644
--- a/src/tracks/ui/TimeShiftHandle.h
+++ b/src/tracks/ui/TimeShiftHandle.h
@@ -11,6 +11,7 @@ Paul Licameli
 #ifndef __AUDACITY_TIMESHIFT_HANDLE__
 #define __AUDACITY_TIMESHIFT_HANDLE__
 
+#include <functional>
 #include <unordered_map>
 
 #include "../../AttachedVirtualFunction.h"
@@ -22,6 +23,7 @@ using TrackArray = std::vector<Track*>;
 class TrackList;
 
 class Track;
+class TrackInterval;
 
 //! Abstract base class for policies to manipulate a track type with the Time Shift tool
 class TrackShifter {
@@ -29,6 +31,29 @@ public:
    virtual ~TrackShifter() = 0;
    //! There is always an associated track
    virtual Track &GetTrack() const = 0;
+
+   using Intervals = std::vector<TrackInterval>;
+
+   //! Return special intervals of the track that will not move
+   const Intervals &FixedIntervals() const { return mFixed; }
+
+   //! Return special intervals of the track that may move
+   const Intervals &MovingIntervals() const { return mMoving; }
+   
+   //! Change intervals satisfying a predicate from fixed to moving
+   void UnfixIntervals(
+      std::function< bool( const TrackInterval& ) > pred );
+
+   //! Change all intervals from fixed to moving
+   void UnfixAll();
+
+protected:
+   //! Derived class constructor can initialize all intervals reported by the track as fixed, none moving
+   /*! This can't be called by the base class constructor, when GetTrack() isn't yet callable */
+   void InitIntervals();
+
+   Intervals mFixed;
+   Intervals mMoving;
 };
 
 //! Used in default of other reimplementations to shift any track as a whole, invoking Track::Offset()