diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,6 +1,15 @@
 Changelog
 =========
 
+Version 0.4.1.2
+---------------
+
+*January 29, 2023*
+
+<https://github.com/mstksg/functor-combinators/releases/tag/v0.4.1.2>
+
+*   Add Invariant instances to Freer.Church types
+
 Version 0.4.1.1
 ---------------
 
diff --git a/functor-combinators.cabal b/functor-combinators.cabal
--- a/functor-combinators.cabal
+++ b/functor-combinators.cabal
@@ -7,7 +7,7 @@
 -- hash: c98f05061d45352f630dd964c7671a2a414e5708a12f8f4f8a39d61b986f6f5d
 
 name:           functor-combinators
-version:        0.4.1.1
+version:        0.4.1.2
 synopsis:       Tools for functor combinator-based program design
 description:    Tools for working with /functor combinators/: types that take functors (or
                 other indexed types) and returns a new functor that "enhances" or "mixes"
diff --git a/src/Control/Monad/Freer/Church.hs b/src/Control/Monad/Freer/Church.hs
--- a/src/Control/Monad/Freer/Church.hs
+++ b/src/Control/Monad/Freer/Church.hs
@@ -36,7 +36,6 @@
   ) where
 
 import           Control.Applicative
-import           Data.Functor.Plus
 import           Control.Monad
 import           Control.Natural
 import           Data.Foldable
@@ -44,6 +43,8 @@
 import           Data.Functor.Bind
 import           Data.Functor.Classes
 import           Data.Functor.Coyoneda
+import           Data.Functor.Invariant
+import           Data.Functor.Plus
 import           Data.Pointed
 import           Data.Semigroup.Foldable
 import           Data.Semigroup.Traversable
@@ -91,6 +92,10 @@
 instance Functor (Free f) where
     fmap f x = Free $ \p b -> runFree x (p . f) b
 
+-- | @since 0.4.1.2
+instance Invariant (Free f) where
+    invmap f _ = fmap f
+
 instance Apply (Free f) where
     (<.>) = ap
 
@@ -238,6 +243,10 @@
 instance Functor (Free1 f) where
     fmap f x = Free1 $ \p b -> runFree1 x (\y c -> p y (f . c)) b
 
+-- | @since 0.4.1.2
+instance Invariant (Free1 f) where
+    invmap f _ = fmap f
+
 instance Apply (Free1 f) where
     (<.>) = apDefault
 
@@ -428,6 +437,10 @@
 
 instance Functor g => Functor (Comp f g) where
     fmap f (x :>>= h) = x :>>= (fmap f . h)
+
+-- | @since 0.4.1.2
+instance Invariant g => Invariant (Comp f g) where
+    invmap f g (x :>>= h) = x :>>= (invmap f g . h)
 
 -- | @since 0.3.6.0
 instance (Apply f, Apply g) => Apply (Comp f g) where