diff --git a/midi-util.cabal b/midi-util.cabal
--- a/midi-util.cabal
+++ b/midi-util.cabal
@@ -1,5 +1,5 @@
 name:                 midi-util
-version:              0.1
+version:              0.1.1
 synopsis:             Utility functions for processing MIDI files
 description:
   Common high-level tasks when processing MIDI files.
@@ -18,7 +18,7 @@
 license-file:         LICENSE
 homepage:             http://github.com/mtolly/midi-util
 bug-reports:          http://github.com/mtolly/midi-util/issues
-stability:            Unstable; not thoroughly tested yet!
+stability:            Seems to work, passes a few tests
 
 library
   exposed-modules:
diff --git a/src/Sound/MIDI/Util.hs b/src/Sound/MIDI/Util.hs
--- a/src/Sound/MIDI/Util.hs
+++ b/src/Sound/MIDI/Util.hs
@@ -14,10 +14,11 @@
 -- * Tempos
 , readTempo, showTempo
 , makeTempo, applyTempo, unapplyTempo, applyTempoTrack, unapplyTempoTrack
-, TempoMap, makeTempoMap, applyTempoMap, unapplyTempoMap
+, TempoMap, makeTempoMap, tempoMapFromBPS, tempoMapToBPS, applyTempoMap, unapplyTempoMap
 -- * Measures and time signatures
 , readSignature, showSignature
 , MeasureMap, MeasureBeats, MeasureMode(..), measures, makeMeasureMap
+, measureMapFromLengths, measureMapToLengths
 , applyMeasureMap, unapplyMeasureMap
 -- * Track names
 , trackName, setTrackName, readTrackName, showTrackName
@@ -180,14 +181,28 @@
 
 -- | Converts between positions in musical time and real time.
 newtype TempoMap = TempoMap (Map.Map (DoubleKey Beats Seconds) BPS)
+  deriving (Eq, Ord)
 
+instance Show TempoMap where
+  showsPrec p = showsPrec p . tempoMapToBPS
+
 makeTempoMap :: RTB.T Beats E.T -> TempoMap
-makeTempoMap = TempoMap . Map.fromAscList . go 0 0 2 . RTB.mapMaybe readTempo where
+makeTempoMap = tempoMapFromBPS . RTB.mapMaybe readTempo
+
+tempoMapFromBPS :: RTB.T Beats BPS -> TempoMap
+tempoMapFromBPS = TempoMap . Map.fromAscList . go 0 0 2 where
   go :: Beats -> Seconds -> BPS -> RTB.T Beats BPS -> [(DoubleKey Beats Seconds, BPS)]
   go b s bps rtb = (DoubleKey b s, bps) : case RTB.viewL rtb of
     Nothing                 -> []
     Just ((db, bps'), rtb') -> go (b + db) (s + applyTempo bps db) bps' rtb'
 
+tempoMapToBPS :: TempoMap -> RTB.T Beats BPS
+tempoMapToBPS (TempoMap m) = let
+  f (DoubleKey bts _, bps) = (bts, bps)
+  f _                      = error
+    "Sound.MIDI.Util.tempoMapToBPS: internal error! TempoMap key wasn't DoubleKey"
+  in RTB.fromAbsoluteEventList $ ATB.fromPairList $ map f $ Map.toAscList m
+
 applyTempoMap :: TempoMap -> Beats -> Seconds
 applyTempoMap (TempoMap tm) bts = case Map.lookupLE (LookupA bts) tm of
   Just (DoubleKey b s, bps) -> s + applyTempo bps (bts - b)
@@ -213,7 +228,11 @@
 -- | Converts between a simple beat position,
 -- and a measure offset plus a beat position.
 newtype MeasureMap = MeasureMap (Map.Map (DoubleKey Beats Int) Beats)
+  deriving (Eq, Ord)
 
+instance Show MeasureMap where
+  showsPrec p = showsPrec p . measureMapToLengths
+
 -- | A number of measures (starting from 0), and an offset within that measure
 -- (also starting from 0).
 type MeasureBeats = (Int, Beats)
@@ -231,7 +250,10 @@
 
 -- | Computes the measure map, given the tempo track from the MIDI.
 makeMeasureMap :: MeasureMode -> RTB.T Beats E.T -> MeasureMap
-makeMeasureMap mm = MeasureMap . Map.fromAscList . go 0 0 4 . RTB.mapMaybe readSignature where
+makeMeasureMap mm = measureMapFromLengths mm . RTB.mapMaybe readSignature
+
+measureMapFromLengths :: MeasureMode -> RTB.T Beats Beats -> MeasureMap
+measureMapFromLengths mm = MeasureMap . Map.fromAscList . go 0 0 4 where
   go :: Beats -> Int -> Beats -> RTB.T Beats Beats -> [(DoubleKey Beats Int, Beats)]
   go b m tsig rtb = (DoubleKey b m, tsig) : case RTB.viewL rtb of
     Nothing                  -> []
@@ -250,6 +272,13 @@
           leftoverBeats = leftoverMsrs * tsig
           truncated = (DoubleKey (b + measures dm tsig) (m + dm), leftoverBeats)
           in truncated : go (b + db) (m + dm + 1) tsig' rtb'
+
+measureMapToLengths :: MeasureMap -> RTB.T Beats Beats
+measureMapToLengths (MeasureMap m) = let
+  f (DoubleKey bts _, len) = (bts, len)
+  f _                      = error
+    "Sound.MIDI.Util.measureMapToLengths: internal error! MeasureMap key wasn't DoubleKey"
+  in RTB.fromAbsoluteEventList $ ATB.fromPairList $ map f $ Map.toAscList m
 
 -- | Uses the measure map to compute which measure a beat position is in.
 applyMeasureMap :: MeasureMap -> Beats -> MeasureBeats