diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # Revision history for timestats
 
+## 0.2.0 -- 2024-05-24
+
+* Expose `Debug.TimeStats.measureMWithLiftIO`.
+
 ## 0.1.4.1 -- 2024-05-23
 
 * Add `Debug.TimeStats.Unsafe.unsafeMeasureM` to measure in some more monads.
diff --git a/src/Debug/TimeStats.hs b/src/Debug/TimeStats.hs
--- a/src/Debug/TimeStats.hs
+++ b/src/Debug/TimeStats.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE RankNTypes #-}
 -- | A module to collect aggregates on how much time is spent in a computation
 --
 -- Aggregates can be identified with a label that determines where the time of
@@ -25,9 +26,10 @@
     -- but they can be handy to implement other measuring primitives.
     --
   , TimeStatsRef
+  , enabled
   , lookupTimeStatsRef
+  , measureMWithLiftIO
   , updateTimeStatsRef
-  , enabled
   ) where
 
 import Control.Exception (evaluate)
@@ -71,13 +73,19 @@
 --
 {-# INLINE measureM #-}
 measureM :: MonadIO m => String -> m a -> m a
-measureM label =
+measureM label = measureMWithLiftIO label liftIO
+
+-- | Like 'measureM' but allows to change the function to lift IO into the
+-- monad.
+{-# INLINE measureMWithLiftIO #-}
+measureMWithLiftIO :: Monad m => String -> (forall b. IO b -> m b) -> m a -> m a
+measureMWithLiftIO label lift =
     -- See the documentation of 'enabled'
     if enabled then do
           -- @ref@ is the reference to the stats associated to the label.
           -- See note [Looking up stats with unsafePerformIO]
       let ref = unsafePerformIO $ lookupTimeStatsRef label
-       in \action -> measureMWith ref action
+       in \action -> measureMWithRef lift ref action
     else
       id
 
@@ -232,12 +240,12 @@
 newTimeStatsRef = liftIO $ TimeStatsRef <$> newIORef initialTimeStats
 
 -- | Measure the time it takes to run the given action and update with it
--- the given reference to time stats.
-measureMWith :: MonadIO m => TimeStatsRef -> m a -> m a
-measureMWith tref m = do
-    t0 <- liftIO getMonotonicTimeNSec
+-- the given reference to time stats, using the given IO lifting function.
+measureMWithRef :: Monad m => (forall b. IO b -> m b) -> TimeStatsRef -> m a -> m a
+measureMWithRef lift tref m = do
+    t0 <- lift getMonotonicTimeNSec
     a <- m
-    liftIO $ do
+    lift $ do
       tf <- getMonotonicTimeNSec
       updateTimeStatsRef tref $ \st ->
         st
diff --git a/src/Debug/TimeStats/Unsafe.hs b/src/Debug/TimeStats/Unsafe.hs
--- a/src/Debug/TimeStats/Unsafe.hs
+++ b/src/Debug/TimeStats/Unsafe.hs
@@ -6,83 +6,39 @@
 -- in this module.
 --
 module Debug.TimeStats.Unsafe
-  ( -- * Measuring
-    unsafeMeasureM
+  ( unsafeMeasureM
   ) where
 
 import Debug.TimeStats
-         ( TimeStats(..)
-         , TimeStatsRef
-         , enabled
-         , lookupTimeStatsRef
-         , updateTimeStatsRef
+         ( lookupTimeStatsRef
+         , measureMWithLiftIO
          )
 import GHC.Clock (getMonotonicTimeNSec)
 import System.IO.Unsafe (unsafePerformIO)
 
--- | Measure the time it takes to run the action.
---
--- Add the time to the stats of the given label and increase its count by one.
---
--- 'measureM' keeps the stats in a globally available store in order to minimize
--- the changes necessary when instrumenting a program. Otherwise a reference to
--- the store would need to be passed to every function that might invoke
--- functions that need this reference.
---
--- A time measure isn't collected if the given action fails with an exception.
--- This is a deliberate choice to demand less of the monad in which measures are
--- taken.
---
--- Time measures aren't collected either if the environment variable
--- @DEBUG_TIMESTATS_ENABLE@ isn't set the first time this function is
--- evaluated.
+-- | Like 'Debug.TimeStats.measureM' but can measure other monads.
 --
 -- This function relies on a hack to perform IO in any monad, which does not
--- always work. In particular, we can expect it to fail in monads where
+-- always work. In particular, we can expect it to miss time in monads where
 --
--- > (m >>= \_ -> undefined) == undefined -- for some computation m
+-- > seq (m >>= \_ -> undefined) () == undefined -- for some computation m
 --
 -- An example of such a monad is the list monad
 --
--- > ([()] >>= \_ -> undefined) == undefined
---
--- Another example is the @Control.Monad.Free.Free IO@.
+-- > seq ([()] >>= \_ -> undefined) () == undefined
 --
--- > (Control.Monad.Free.Pure () >>= \_ -> undefined) == undefined
+-- Another example is the monad @Control.Monad.Free.Free f@.
 --
--- But it seems to work on @IO@ or @ReaderT IO@.
+-- > seq (return () >>= \_ -> undefined :: Free IO ()) () == undefined
 --
--- > seq (print () >>= \_ -> undefined) () == ()
+-- But it seems to work in monads with state like @IO@, @ReaderT IO@, and
+-- @Control.Monad.State.State s@.
 --
--- Also, monads that run the continuation of bind multiple times might only
--- have accounted the time to run the first time only.
+-- > seq (return () >>= \_ -> undefined :: YourMonadHere ()) () == ()
 --
 {-# INLINE unsafeMeasureM #-}
 unsafeMeasureM :: Monad m => String -> m a -> m a
-unsafeMeasureM label =
-    -- See the documentation of 'enabled'
-    if enabled then do
-          -- @ref@ is the reference to the stats associated to the label.
-          -- See note [Looking up stats with unsafePerformIO]
-      let ref = unsafePerformIO $ lookupTimeStatsRef label
-       in \action -> measureMWith ref action
-    else
-      id
-
--- | Measure the time it takes to run the given action and update with it
--- the given reference to time stats.
-measureMWith :: Monad m => TimeStatsRef -> m a -> m a
-measureMWith tref m = do
-    t0 <- intersperseIOinM getMonotonicTimeNSec
-    a <- m
-    intersperseIOinM $ do
-      tf <- getMonotonicTimeNSec
-      updateTimeStatsRef tref $ \st ->
-        st
-          { timeStat = (tf - t0) + timeStat st
-          , countStat = 1 + countStat st
-          }
-    return a
+unsafeMeasureM label = measureMWithLiftIO label intersperseIOinM
 
 ---------------------
 -- intersperseIOinM
diff --git a/timestats.cabal b/timestats.cabal
--- a/timestats.cabal
+++ b/timestats.cabal
@@ -1,6 +1,6 @@
 cabal-version:      2.4
 name:               timestats
-version:            0.1.4.1
+version:            0.2.0
 
 synopsis: A library for profiling time in Haskell applications