diff --git a/Control/Monad/Invert.hs b/Control/Monad/Invert.hs
index 6eb791a..f322b75 100644
--- a/Control/Monad/Invert.hs
+++ b/Control/Monad/Invert.hs
@@ -9,6 +9,7 @@ module Control.Monad.Invert
     , unblock
     , bracket
     , bracket_
+    , onException
       -- * Memory allocation
     , alloca
     , allocaBytes
@@ -29,8 +30,9 @@ import Foreign.Storable (Storable)
 import Foreign.Ptr (Ptr)
 import Foreign.ForeignPtr (ForeignPtr)
 import qualified Foreign.ForeignPtr as F
+import Control.Monad.IO.Class (MonadIO)
 
-class Monad m => MonadInvertIO m where
+class MonadIO m => MonadInvertIO m where
     data InvertedIO m :: * -> *
     type InvertedArg m
     invertIO :: m a -> InvertedArg m -> IO (InvertedIO m a)
@@ -81,6 +83,10 @@ finally :: MonadInvertIO m => m a -> m b -> m a
 finally action after =
     revertIO $ \a -> invertIO action a `E.finally` invertIO after a
 
+onException :: MonadInvertIO m => m a -> m b -> m a
+onException action after =
+    revertIO $ \a -> invertIO action a `E.onException` invertIO after a
+
 catch :: (E.Exception e, MonadInvertIO m) => m a -> (e -> m a) -> m a
 catch action handler =
     revertIO $ \a -> invertIO action a `E.catch` (\e -> invertIO (handler e) a)
diff --git a/runtests.hs b/runtests.hs
index c71b157..7f4b955 100644
--- a/runtests.hs
+++ b/runtests.hs
@@ -43,6 +43,7 @@ testSuite s run = testGroup s
     -- FIXME test block and unblock
     , testCase "bracket" $ case_bracket run
     , testCase "bracket_" $ case_bracket_ run
+    , testCase "onException" $ case_onException run
     ]
 
 ignore :: IO () -> IO ()
@@ -98,6 +99,20 @@ case_bracket_ run = do
     j <- readIORef i
     j @?= 4
 
+case_onException :: (MonadIO m, MonadInvertIO m) => (m () -> IO ()) -> Assertion
+case_onException run = do
+    i <- newIORef one
+    ignore $ run $ onException
+        (liftIO (writeIORef i 2) >> error "ignored")
+        (liftIO $ writeIORef i 3)
+    j <- readIORef i
+    j @?= 3
+    ignore $ run $ onException
+        (liftIO $ writeIORef i 4)
+        (liftIO $ writeIORef i 5)
+    k <- readIORef i
+    k @?= 4
+
 case_throwError :: Assertion
 case_throwError = do
     i <- newIORef one