diff --git a/Control/Comonad/Env.hs b/Control/Comonad/Env.hs
--- a/Control/Comonad/Env.hs
+++ b/Control/Comonad/Env.hs
@@ -7,31 +7,9 @@
 -- Maintainer  :  Edward Kmett <ekmett@gmail.com>
 -- Stability   :  experimental
 -- Portability :  non-portable (fundeps, MPTCs)
---
--- The Env comonad (aka the Coreader, Environment, or Product comonad)
--- 
--- A co-Kleisli arrow in the Env comonad is isomorphic to a Kleisli arrow
--- in the reader monad.
---
--- (a -> e -> m) ~ (a, e) -> m ~ Env e a -> m
 ----------------------------------------------------------------------------
 module Control.Comonad.Env ( 
-  -- * ComonadEnv class
-    ComonadEnv(..)
-  , asks
-  -- * The Env comonad
-  , Env
-  , env
-  , runEnv
-  -- * The EnvT comonad transformer
-  , EnvT(..)
-  , runEnvT
-  -- * Re-exported modules
-  , module Control.Comonad
-  , module Control.Comonad.Trans.Class
+    module Control.Comonad.Env.Lazy
   ) where
 
-import Control.Comonad
-import Control.Comonad.Env.Class (ComonadEnv(..), asks)
-import Control.Comonad.Trans.Class
-import Control.Comonad.Trans.Env (Env, env, runEnv, EnvT(..), runEnvT)
+import Control.Comonad.Env.Lazy
diff --git a/Control/Comonad/Env/Lazy.hs b/Control/Comonad/Env/Lazy.hs
new file mode 100644
--- /dev/null
+++ b/Control/Comonad/Env/Lazy.hs
@@ -0,0 +1,38 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Control.Comonad.Env.Lazy
+-- Copyright   :  (C) 2008-2011 Edward Kmett
+-- License     :  BSD-style (see the file LICENSE)
+--
+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Stability   :  experimental
+-- Portability :  non-portable (fundeps, MPTCs)
+--
+-- The Env comonad (aka the Coreader, Environment, or Product comonad)
+-- 
+-- A co-Kleisli arrow in the Env comonad is isomorphic to a Kleisli arrow
+-- in the reader monad.
+--
+-- (a -> e -> m) ~ (a, e) -> m ~ Env e a -> m
+----------------------------------------------------------------------------
+module Control.Comonad.Env.Lazy ( 
+  -- * ComonadEnv class
+    ComonadEnv(..)
+  , asks
+  , local
+  -- * The Env comonad
+  , Env
+  , env
+  , runEnv
+  -- * The EnvT comonad transformer
+  , EnvT(..)
+  , runEnvT
+  -- * Re-exported modules
+  , module Control.Comonad
+  , module Control.Comonad.Trans.Class
+  ) where
+
+import Control.Comonad
+import Control.Comonad.Env.Class (ComonadEnv(..), asks)
+import Control.Comonad.Trans.Class
+import Control.Comonad.Trans.Env.Lazy (Env, env, runEnv, EnvT(..), runEnvT, local)
diff --git a/Control/Comonad/Env/Strict.hs b/Control/Comonad/Env/Strict.hs
new file mode 100644
--- /dev/null
+++ b/Control/Comonad/Env/Strict.hs
@@ -0,0 +1,38 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Control.Comonad.Env.Strict
+-- Copyright   :  (C) 2008-2011 Edward Kmett
+-- License     :  BSD-style (see the file LICENSE)
+--
+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Stability   :  experimental
+-- Portability :  non-portable (fundeps, MPTCs)
+--
+-- The Env comonad (aka the Coreader, Environment, or Product comonad)
+-- 
+-- A co-Kleisli arrow in the Env comonad is isomorphic to a Kleisli arrow
+-- in the reader monad.
+--
+-- (a -> e -> m) ~ (a, e) -> m ~ Env e a -> m
+----------------------------------------------------------------------------
+module Control.Comonad.Env.Strict ( 
+  -- * ComonadEnv class
+    ComonadEnv(..)
+  , asks
+  , local
+  -- * The Env comonad
+  , Env
+  , env
+  , runEnv
+  -- * The EnvT comonad transformer
+  , EnvT(..)
+  , runEnvT
+  -- * Re-exported modules
+  , module Control.Comonad
+  , module Control.Comonad.Trans.Class
+  ) where
+
+import Control.Comonad
+import Control.Comonad.Env.Class (ComonadEnv(..), asks)
+import Control.Comonad.Trans.Class
+import Control.Comonad.Trans.Env.Strict (Env, env, runEnv, EnvT(..), runEnvT, local)
diff --git a/Control/Comonad/Identity.hs b/Control/Comonad/Identity.hs
new file mode 100644
--- /dev/null
+++ b/Control/Comonad/Identity.hs
@@ -0,0 +1,19 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Control.Comonad.Identity
+-- Copyright   :  (C) 2008-2011 Edward Kmett
+-- License     :  BSD-style (see the file LICENSE)
+--
+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Stability   :  experimental
+-- Portability :  non-portable (fundeps, MPTCs)
+----------------------------------------------------------------------------
+module Control.Comonad.Identity ( 
+    module Control.Comonad
+  , module Data.Functor.Identity
+  , module Control.Comonad.Trans.Identity
+  ) where
+
+import Control.Comonad
+import Data.Functor.Identity
+import Control.Comonad.Trans.Identity
diff --git a/Control/Comonad/Store.hs b/Control/Comonad/Store.hs
--- a/Control/Comonad/Store.hs
+++ b/Control/Comonad/Store.hs
@@ -9,23 +9,7 @@
 -- Portability :  non-portable (fundeps, MPTCs)
 ----------------------------------------------------------------------------
 module Control.Comonad.Store ( 
-  -- * ComonadStore class
-    ComonadStore(..)
-  , gets
-  , experiment
-  -- * The Store comonad
-  , Store
-  , store
-  , runStore
-  -- * The StoreT comonad transformer
-  , StoreT(..)
-  , runStoreT
-  -- * Re-exported modules
-  , module Control.Comonad
-  , module Control.Comonad.Trans.Class
+  module Control.Comonad.Store.Lazy
   ) where
 
-import Control.Comonad
-import Control.Comonad.Store.Class (ComonadStore(..), gets, experiment)
-import Control.Comonad.Trans.Class
-import Control.Comonad.Trans.Store (Store, store, runStore, StoreT(..), runStoreT)
+import Control.Comonad.Store.Lazy
diff --git a/Control/Comonad/Store/Lazy.hs b/Control/Comonad/Store/Lazy.hs
new file mode 100644
--- /dev/null
+++ b/Control/Comonad/Store/Lazy.hs
@@ -0,0 +1,31 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Control.Comonad.Store.Lazy
+-- Copyright   :  (C) 2008-2011 Edward Kmett
+-- License     :  BSD-style (see the file LICENSE)
+--
+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Stability   :  experimental
+-- Portability :  non-portable (fundeps, MPTCs)
+----------------------------------------------------------------------------
+module Control.Comonad.Store.Lazy ( 
+  -- * ComonadStore class
+    ComonadStore(..)
+  , gets
+  , experiment
+  -- * The Store comonad
+  , Store
+  , store
+  , runStore
+  -- * The StoreT comonad transformer
+  , StoreT(..)
+  , runStoreT
+  -- * Re-exported modules
+  , module Control.Comonad
+  , module Control.Comonad.Trans.Class
+  ) where
+
+import Control.Comonad
+import Control.Comonad.Store.Class (ComonadStore(..), gets, experiment)
+import Control.Comonad.Trans.Class
+import Control.Comonad.Trans.Store.Lazy (Store, store, runStore, StoreT(..), runStoreT)
diff --git a/Control/Comonad/Store/Strict.hs b/Control/Comonad/Store/Strict.hs
new file mode 100644
--- /dev/null
+++ b/Control/Comonad/Store/Strict.hs
@@ -0,0 +1,31 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Control.Comonad.Store.Strict
+-- Copyright   :  (C) 2008-2011 Edward Kmett
+-- License     :  BSD-style (see the file LICENSE)
+--
+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Stability   :  experimental
+-- Portability :  non-portable (fundeps, MPTCs)
+----------------------------------------------------------------------------
+module Control.Comonad.Store.Strict ( 
+  -- * ComonadStore class
+    ComonadStore(..)
+  , gets
+  , experiment
+  -- * The Store comonad
+  , Store
+  , store
+  , runStore
+  -- * The StoreT comonad transformer
+  , StoreT(..)
+  , runStoreT
+  -- * Re-exported modules
+  , module Control.Comonad
+  , module Control.Comonad.Trans.Class
+  ) where
+
+import Control.Comonad
+import Control.Comonad.Store.Class (ComonadStore(..), gets, experiment)
+import Control.Comonad.Trans.Class
+import Control.Comonad.Trans.Store.Strict (Store, store, runStore, StoreT(..), runStoreT)
diff --git a/comonads-fd.cabal b/comonads-fd.cabal
--- a/comonads-fd.cabal
+++ b/comonads-fd.cabal
@@ -1,6 +1,6 @@
 name:          comonads-fd
 category:      Control, Comonads
-version:       0.1.1
+version:       0.4
 license:       BSD3
 cabal-version: >= 1.2
 license-file:  LICENSE
@@ -17,14 +17,19 @@
   build-depends: 
     base >= 4 && < 4.4,
     transformers >= 0.2.0 && < 0.3,
-    comonad >= 0.1.1 && < 0.2,
-    comonad-transformers >= 0.1 && < 0.2
+    comonad >= 0.4 && < 0.5,
+    comonad-transformers >= 0.4 && < 0.5
 
   exposed-modules:
     Control.Comonad.Env
     Control.Comonad.Env.Class
+    Control.Comonad.Env.Strict
+    Control.Comonad.Env.Lazy
+    Control.Comonad.Identity
     Control.Comonad.Store
     Control.Comonad.Store.Class
+    Control.Comonad.Store.Strict
+    Control.Comonad.Store.Lazy
     Control.Comonad.Traced
     Control.Comonad.Traced.Class
 
