diff --git a/alignment.cabal b/alignment.cabal
--- a/alignment.cabal
+++ b/alignment.cabal
@@ -1,7 +1,7 @@
 -- documentation, see http://haskell.org/cabal/users-guide/
 
 name:                   alignment
-version:                0.1.0.2
+version:                0.1.0.3
 synopsis:               Zip-alignment
 description:
   <<https://system-f.gitlab.io/logo/systemf-450x450.jpg>>
diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,7 @@
+0.1.0.3
+
+* Change the type of `alignWith` to be more consistent.
+
 0.1.0.2
 
 * Add `allThoseAOr` and `allThoseBOr`.
diff --git a/src/Data/Alignment.hs b/src/Data/Alignment.hs
--- a/src/Data/Alignment.hs
+++ b/src/Data/Alignment.hs
@@ -169,16 +169,27 @@
     -> f b
     -> This f a b
   align =
-    alignWith (\x -> x) (\x -> x)
+    alignWith (\x -> x) (\x -> x) (\x -> x)
   alignWith ::
-    (a -> c)
+    ((a, b) -> (c, d))
+    -> (a -> c)
     -> (b -> d)
     -> f a
     -> f b
     -> This f c d
-  alignWith f g a b =
-    bimap f g (align a b)
+  alignWith f g h t1 t2 =
+    case align t1 t2 of
+      This t r ->
+        This (fmap f t) (fmap (bimap (fmap g) (fmap h)) r)
   {-# MINIMAL align | alignWith #-}
+  alignWith' ::
+    (a -> c)
+    -> (b -> d)
+    -> f a
+    -> f b
+    -> This f c d
+  alignWith' f g =
+    alignWith (bimap f g) f g
 
 -- |
 --