diff --git a/src/Network/Wai/Trans.hs b/src/Network/Wai/Trans.hs
--- a/src/Network/Wai/Trans.hs
+++ b/src/Network/Wai/Trans.hs
@@ -31,23 +31,22 @@
 
 import           Network.Wai as X
 
-import           Data.Function.Syntax
 import           Control.Monad.IO.Class
 
-
-type ApplicationT m = Request -> (Response -> IO ResponseReceived) -> m ResponseReceived
+-- | Isomorphic to @Kleisli (ContT ResponseReceived m) Request Response@
+type ApplicationT m = Request -> (Response -> m ResponseReceived) -> m ResponseReceived
 type MiddlewareT m = ApplicationT m -> ApplicationT m
 
 
-liftApplication :: MonadIO m => Application -> ApplicationT m
-liftApplication app = liftIO .* app
+liftApplication :: MonadIO m => (forall a. m a -> IO a) -> Application -> ApplicationT m
+liftApplication run app req resp = liftIO (app req (run . resp))
 
-liftMiddleware :: MonadIO m => (ApplicationT m -> Application) -> Middleware -> MiddlewareT m
-liftMiddleware runAppT mid app = liftApplication $ mid (runAppT app)
+liftMiddleware :: MonadIO m => (forall a. m a -> IO a) -> Middleware -> MiddlewareT m
+liftMiddleware run mid app = liftApplication run (mid (runApplicationT run app))
 
-runApplicationT :: (forall a. m a -> IO a) -> ApplicationT m -> Application
-runApplicationT run app req respond = run (app req respond)
+runApplicationT :: MonadIO m => (forall a. m a -> IO a) -> ApplicationT m -> Application
+runApplicationT run app req respond = run (app req (liftIO . respond))
 
 runMiddlewareT :: MonadIO m => (forall a. m a -> IO a) -> MiddlewareT m -> Middleware
-runMiddlewareT run mid app req respond = run (mid (liftApplication app) req respond)
+runMiddlewareT run mid app = runApplicationT run (mid (liftApplication run app))
 
diff --git a/wai-transformers.cabal b/wai-transformers.cabal
--- a/wai-transformers.cabal
+++ b/wai-transformers.cabal
@@ -1,5 +1,5 @@
 Name:                   wai-transformers
-Version:                0.0.2
+Version:                0.0.3
 Author:                 Athan Clark <athan.clark@gmail.com>
 Maintainer:             Athan Clark <athan.clark@gmail.com>
 License:                BSD3
@@ -16,7 +16,6 @@
   GHC-Options:          -Wall
   Exposed-Modules:      Network.Wai.Trans
   Build-Depends:        base >= 4.6 && < 5
-                      , composition-extra >= 2.0.0
                       , wai
                       , transformers