diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,9 @@
+4.0
+---
+* Updated to work with `semigroupoids` and `comonad` 4.0
+* `instance ComonadCofree Maybe NonEmpty`
+* `instance ComonadCofree (Const b) ((,) b)`
+
 3.4.2
 -----
 * Generalized `liftF`.
diff --git a/free.cabal b/free.cabal
--- a/free.cabal
+++ b/free.cabal
@@ -1,6 +1,6 @@
 name:          free
 category:      Control, Monads
-version:       3.4.2
+version:       4.0
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
@@ -52,17 +52,15 @@
     GADTs
 
   build-depends:
-    base                 >= 4       && < 5,
-    bifunctors           >= 3,
+    base                 == 4.*,
+    bifunctors           == 3.*,
+    comonad              == 4.*,
     distributive         >= 0.2.1,
-    transformers         >= 0.2.0   && < 0.4,
     mtl                  >= 2.0.1.0 && < 2.2,
-    semigroupoids        >= 3,
-    comonad              >= 3,
-    comonad-transformers >= 3,
-    comonads-fd          >= 3,
-    semigroups           >= 0.8.3.1,
-    profunctors          >= 3.2     && < 4
+    profunctors          == 4.*,
+    semigroupoids        == 4.*,
+    semigroups           >= 0.8.3.1 && < 1,
+    transformers         >= 0.2.0   && < 0.4
 
   if impl(ghc)
     cpp-options: -DGHC_TYPEABLE
diff --git a/src/Control/Comonad/Cofree/Class.hs b/src/Control/Comonad/Cofree/Class.hs
--- a/src/Control/Comonad/Cofree/Class.hs
+++ b/src/Control/Comonad/Cofree/Class.hs
@@ -22,12 +22,20 @@
 import Control.Comonad.Trans.Store
 import Control.Comonad.Trans.Traced
 import Control.Comonad.Trans.Identity
+import Data.List.NonEmpty
 import Data.Semigroup
 
 -- | Allows you to peel a layer off a cofree comonad.
 class (Functor f, Comonad w) => ComonadCofree f w | w -> f where
   -- | Remove a layer.
   unwrap :: w a -> f (w a)
+
+instance ComonadCofree Maybe NonEmpty where
+  unwrap (_ :| [])       = Nothing
+  unwrap (_ :| (a : as)) = Just (a :| as)
+
+instance ComonadCofree (Const b) ((,) b) where
+  unwrap = Const . fst
 
 instance ComonadCofree f w => ComonadCofree f (IdentityT w) where
   unwrap = fmap IdentityT . unwrap . runIdentityT
diff --git a/src/Control/Monad/Free.hs b/src/Control/Monad/Free.hs
--- a/src/Control/Monad/Free.hs
+++ b/src/Control/Monad/Free.hs
@@ -32,6 +32,7 @@
 
 import Control.Applicative
 import Control.Monad (liftM, MonadPlus(..))
+import Control.Monad.Fix
 import Control.Monad.Trans.Class
 import Control.Monad.Free.Class
 import Control.Monad.Reader.Class
@@ -86,8 +87,8 @@
 --
 -- This can be very useful for modeling domain specific languages, trees, or other constructs.
 --
--- This instance of 'MonadFree' is fairly naive about the encoding. For more efficient free monad implementations that require additional
--- extensions and thus aren't included here, you may want to look at the @kan-extensions@ package.
+-- This instance of 'MonadFree' is fairly naive about the encoding. For more efficient free monad implementation see "Control.Monad.Free.Church", in particular note the 'Control.Monad.Free.Church.improve' combinator.
+-- You may also want to take a look at the @kan-extensions@ package (<http://hackage.haskell.org/package/kan-extensions>).
 --
 -- A number of common monads arise as free monads,
 --
@@ -153,6 +154,9 @@
   {-# INLINE return #-}
   Pure a >>= f = f a
   Free m >>= f = Free ((>>= f) <$> m)
+
+instance Functor f => MonadFix (Free f) where
+  mfix f = a where a = f (impure a); impure (Pure x) = x; impure (Free _) = error "mfix (Free f): Free"
 
 -- | This violates the Alternative laws, handle with care.
 instance Alternative v => Alternative (Free v) where
diff --git a/src/Control/Monad/Free/Class.hs b/src/Control/Monad/Free/Class.hs
--- a/src/Control/Monad/Free/Class.hs
+++ b/src/Control/Monad/Free/Class.hs
@@ -37,7 +37,7 @@
 -- |
 -- Monads provide substitution ('fmap') and renormalization ('Control.Monad.join'):
 --
--- @m '>>=' f = 'Control.Monad.join' . 'fmap' f m@
+-- @m '>>=' f = 'Control.Monad.join' ('fmap' f m)@
 --
 -- A free 'Monad' is one that does no work during the normalization step beyond simply grafting the two monadic values together.
 --
@@ -72,9 +72,11 @@
 -- Or we could choose to program with @'Control.Monad.Free.Free' Pair@ instead of 'Tree'
 -- and thereby avoid having to define our own 'Monad' instance.
 --
--- Moreover, the @kan-extensions@ package provides 'MonadFree' instances that can
--- improve the /asymptotic/ complexity of code that constructors free monads by
--- effectively reassociating the use of ('>>=').
+-- Moreover, "Control.Monad.Free.Church" provides a 'MonadFree'
+-- instance that can improve the /asymptotic/ complexity of code that
+-- constructs free monads by effectively reassociating the use of
+-- ('>>='). You may also want to take a look at the @kan-extensions@
+-- package (<http://hackage.haskell.org/package/kan-extensions>).
 --
 -- See 'Control.Monad.Free.Free' for a more formal definition of the free 'Monad'
 -- for a 'Functor'.