diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,10 @@
 # Revision history for lifted-async
 
+## v0.10.2 - 20201-04-02
+
+* Define withAsync in terms of corresponding function from async ([#36](https://github.com/maoe/lifted-async/pull/36))
+  * Fixes [#34](https://github.com/maoe/lifted-async/issues/34)
+
 ## v0.10.1.3 - 2021-02-26
 
 * Support GHC 9.0.1 ([#33](https://github.com/maoe/lifted-async/pull/33))
diff --git a/lifted-async.cabal b/lifted-async.cabal
--- a/lifted-async.cabal
+++ b/lifted-async.cabal
@@ -1,6 +1,6 @@
 cabal-version:       1.24
 name:                lifted-async
-version:             0.10.1.3
+version:             0.10.2
 synopsis:            Run lifted IO operations asynchronously and wait for their results
 homepage:            https://github.com/maoe/lifted-async
 bug-reports:         https://github.com/maoe/lifted-async/issues
diff --git a/src/Control/Concurrent/Async/Lifted.hs b/src/Control/Concurrent/Async/Lifted.hs
--- a/src/Control/Concurrent/Async/Lifted.hs
+++ b/src/Control/Concurrent/Async/Lifted.hs
@@ -139,7 +139,7 @@
   => m a
   -> (Async (StM m a) -> m b)
   -> m b
-withAsync = withAsyncUsing async
+withAsync = liftWithAsync A.withAsync
 {-# INLINABLE withAsync #-}
 
 -- | Generalized version of 'A.withAsyncBound'.
@@ -148,8 +148,16 @@
   => m a
   -> (Async (StM m a) -> m b)
   -> m b
-withAsyncBound = withAsyncUsing asyncBound
+withAsyncBound = liftWithAsync A.withAsyncBound
 {-# INLINABLE withAsyncBound #-}
+
+liftWithAsync
+  :: MonadBaseControl IO m
+  => (IO (StM m a) -> (Async (StM m a) -> IO (StM m b)) -> IO (StM m b))
+  -> (m a -> (Async (StM m a) -> m b) -> m b)
+liftWithAsync withA action cont = restoreM =<< do
+  liftBaseWith $ \runInIO -> do
+    withA (runInIO action) (runInIO . cont)
 
 -- | Generalized version of 'A.withAsyncOn'.
 withAsyncOn