diff --git a/Data/HashMap/Internal.hs b/Data/HashMap/Internal.hs
index 6cad1028..7726ae32 100644
--- a/Data/HashMap/Internal.hs
+++ b/Data/HashMap/Internal.hs
@@ -126,6 +126,7 @@ module Data.HashMap.Internal
     , nextShift
     , sparseIndex
     , two
+    , two'
     , unionArrayBy
     , updateFullArray
     , updateFullArrayM
@@ -164,7 +165,7 @@ import Data.Hashable              (Hashable)
 import Data.Hashable.Lifted       (Hashable1, Hashable2)
 import Data.HashMap.Internal.List (isPermutationBy, unorderedCompare)
 import Data.Semigroup             (Semigroup (..), stimesIdempotentMonoid)
-import GHC.Exts                   (Int (..), Int#, TYPE, (==#))
+import GHC.Exts                   (Int (..), Int#, TYPE, Word (..), (==#))
 import GHC.Stack                  (HasCallStack)
 import Prelude                    hiding (Foldable (..), filter, lookup, map,
                                    pred)
@@ -832,7 +833,7 @@ insert' h0 k0 v0 m0 = go h0 k0 v0 0 m0
       where i = index h s
     go h k x s t@(Collision hy v)
         | h == hy   = Collision h (updateOrSnocWith (\a _ -> (# a #)) k x v)
-        | otherwise = go h k x s $ BitmapIndexed (mask hy s) (A.singleton t)
+        | otherwise = runST (two s h k x hy t)
 {-# INLINABLE insert' #-}
 
 -- | Insert optimized for the case when we know the key is not in the map.
@@ -866,8 +867,7 @@ insertNewKey !h0 !k0 x0 !m0 = go h0 k0 x0 0 m0
       where i = index h s
     go h k x s t@(Collision hy v)
         | h == hy   = Collision h (A.snoc v (L k x))
-        | otherwise =
-            go h k x s $ BitmapIndexed (mask hy s) (A.singleton t)
+        | otherwise = runST (two s h k x hy t)
 {-# NOINLINE insertNewKey #-}
 
 
@@ -884,33 +884,19 @@ insertKeyExists !collPos0 !h0 !k0 x0 !m0 = go collPos0 h0 k0 x0 m0
         = Leaf h (L k x)
     go collPos shiftedHash k x (BitmapIndexed b ary) =
         let !st  = A.index ary i
-            !st' = go collPos (shiftHash shiftedHash) k x st
+            !st' = go collPos (nextSH shiftedHash) k x st
         in BitmapIndexed b (A.update ary i st')
-      where m = mask' shiftedHash
+      where m = maskSH shiftedHash
             i = sparseIndex b m
     go collPos shiftedHash k x (Full ary) =
         let !st  = A.index ary i
-            !st' = go collPos (shiftHash shiftedHash) k x st
+            !st' = go collPos (nextSH shiftedHash) k x st
         in Full (updateFullArray ary i st')
-      where i = index' shiftedHash
+      where i = indexSH shiftedHash
     go collPos _shiftedHash k x (Collision h v)
         | collPos >= 0 = Collision h (setAtPosition collPos k x v)
         | otherwise = Empty -- error "Internal error: go {collPos negative}"
     go _ _ _ _ Empty = Empty -- error "Internal error: go Empty"
-
-    -- Customized version of 'index' that doesn't require a 'Shift'.
-    index' :: Hash -> Int
-    index' w = fromIntegral $ w .&. subkeyMask
-    {-# INLINE index' #-}
-
-    -- Customized version of 'mask' that doesn't require a 'Shift'.
-    mask' :: Word -> Bitmap
-    mask' w = 1 `unsafeShiftL` index' w
-    {-# INLINE mask' #-}
-
-    shiftHash h = h `unsafeShiftR` bitsPerSubkey
-    {-# INLINE shiftHash #-}
-
 {-# NOINLINE insertKeyExists #-}
 
 -- | Replace the ith Leaf with Leaf k v.
@@ -953,44 +939,52 @@ unsafeInsert k0 v0 m0 = runST (go h0 k0 v0 0 m0)
       where i = index h s
     go h k x s t@(Collision hy v)
         | h == hy   = return $! Collision h (updateOrSnocWith (\a _ -> (# a #)) k x v)
-        | otherwise = go h k x s $ BitmapIndexed (mask hy s) (A.singleton t)
+        | otherwise = two s h k x hy t
 {-# INLINABLE unsafeInsert #-}
 
--- | Create a map from two key-value pairs which hashes don't collide. To
--- enhance sharing, the second key-value pair is represented by the hash of its
--- key and a singleton HashMap pairing its key with its value.
+-- | Create a map from a key-value pair and a 'Leaf' or 'Collision' node with a
+-- different hash.
 --
--- Note: to avoid silly thunks, this function must be strict in the
--- key. See issue #232. We don't need to force the HashMap argument
--- because it's already in WHNF (having just been matched) and we
--- just put it directly in an array.
+-- It is the caller's responsibility to ensure that the HashMap argument is in
+-- WHNF.
 two :: Shift -> Hash -> k -> v -> Hash -> HashMap k v -> ST s (HashMap k v)
-two = go
-  where
-    go s h1 k1 v1 h2 t2
-        | bp1 == bp2 = do
-            st <- go (nextShift s) h1 k1 v1 h2 t2
-            ary <- A.singletonM st
-            return $ BitmapIndexed bp1 ary
-        | otherwise  = do
-            mary <- A.new 2 $! Leaf h1 (L k1 v1)
-            A.write mary idx2 t2
-            ary <- A.unsafeFreeze mary
-            return $ BitmapIndexed (bp1 .|. bp2) ary
-      where
-        bp1  = mask h1 s
-        bp2  = mask h2 s
-        !(I# i1) = index h1 s
-        !(I# i2) = index h2 s
-        idx2 = I# (i1 Exts.<# i2)
-        -- This way of computing idx2 saves us a branch compared to the previous approach:
-        --
-        -- idx2 | index h1 s < index h2 s = 1
-        --      | otherwise               = 0
-        --
-        -- See https://github.com/haskell-unordered-containers/unordered-containers/issues/75#issuecomment-1128419337
+two s h1 k1 v1 = two' s h1 l
+  where !l = Leaf h1 (L k1 v1)
 {-# INLINE two #-}
 
+-- | Create a map from two 'Leaf' or 'Collision' nodes whose hashes are
+-- distinct.
+--
+-- It is the caller's responsibility to ensure that both HashMap arguments are
+-- in WHNF.
+two' :: Shift -> Hash -> HashMap k v -> Hash -> HashMap k v -> ST s (HashMap k v)
+two' s h1 lc1 h2 lc2 = two_go (shiftHash s h1) lc1 (shiftHash s h2) lc2
+{-# INLINE two' #-}
+
+-- | This function lives at the top-level so 'two' and `two'` can be inlined
+-- without inlining this loop.
+two_go :: ShiftedHash -> HashMap k v -> ShiftedHash -> HashMap k v -> ST s (HashMap k v)
+two_go !sh1 t1 !sh2 t2
+    | bp1 == bp2 = do
+        st <- two_go (nextSH sh1) t1 (nextSH sh2) t2
+        ary <- A.singletonM st
+        return $ BitmapIndexed bp1 ary
+    | otherwise  = do
+        mary <- A.new 2 t1
+        A.write mary idx2 t2
+        ary <- A.unsafeFreeze mary
+        return $ BitmapIndexed (bp1 .|. bp2) ary
+  where
+    !bp1@(W# bp1#) = maskSH sh1
+    !bp2@(W# bp2#) = maskSH sh2
+    idx2 = I# (bp1# `Exts.ltWord#` bp2#)
+    -- This way of computing idx2 saves us a branch compared to the previous approach:
+    --
+    -- idx2 | index h1 s < index h2 s = 1
+    --      | otherwise               = 0
+    --
+    -- See https://github.com/haskell-unordered-containers/unordered-containers/issues/75#issuecomment-1128419337
+
 -- | \(O(\log n)\) Associate the value with the key in this map.  If
 -- this map previously contained a mapping for the key, the old value
 -- is replaced by the result of applying the given function to the new
@@ -1050,7 +1044,7 @@ insertModifying x f k0 m0 = go h0 k0 0 m0
             in if A.unsafeSameArray v v'
                then t
                else Collision h v'
-        | otherwise = go h k s $ BitmapIndexed (mask hy s) (A.singleton t)
+        | otherwise = runST (two s h k x hy t)
 {-# INLINABLE insertModifying #-}
 
 -- | Like insertModifying for arrays; used to implement insertModifying
@@ -1109,7 +1103,7 @@ unsafeInsertWithKey f k0 v0 m0 = runST (go h0 k0 v0 0 m0)
       where i = index h s
     go h k x s t@(Collision hy v)
         | h == hy   = return $! Collision h (updateOrSnocWithKey f k x v)
-        | otherwise = go h k x s $ BitmapIndexed (mask hy s) (A.singleton t)
+        | otherwise = two s h k x hy t
 {-# INLINABLE unsafeInsertWithKey #-}
 
 -- | \(O(\log n)\) Remove the mapping for the specified key from this map
@@ -1178,11 +1172,11 @@ delete' h0 k0 m0 = go h0 k0 0 m0
 deleteKeyExists :: Int -> Hash -> k -> HashMap k v -> HashMap k v
 deleteKeyExists !collPos0 !h0 !k0 !m0 = go collPos0 h0 k0 m0
   where
-    go :: Int -> Word -> k -> HashMap k v -> HashMap k v
+    go :: Int -> ShiftedHash -> k -> HashMap k v -> HashMap k v
     go !_collPos !_shiftedHash !_k (Leaf _ _) = Empty
     go collPos shiftedHash k (BitmapIndexed b ary) =
             let !st = A.index ary i
-                !st' = go collPos (shiftHash shiftedHash) k st
+                !st' = go collPos (nextSH shiftedHash) k st
             in case st' of
                 Empty | A.length ary == 1 -> Empty
                       | A.length ary == 2 ->
@@ -1195,18 +1189,18 @@ deleteKeyExists !collPos0 !h0 !k0 !m0 = go collPos0 h0 k0 m0
                       bIndexed = BitmapIndexed (b .&. complement m) (A.delete ary i)
                 l | isLeafOrCollision l && A.length ary == 1 -> l
                 _ -> BitmapIndexed b (A.update ary i st')
-      where m = mask' shiftedHash
+      where m = maskSH shiftedHash
             i = sparseIndex b m
     go collPos shiftedHash k (Full ary) =
         let !st   = A.index ary i
-            !st' = go collPos (shiftHash shiftedHash) k st
+            !st' = go collPos (nextSH shiftedHash) k st
         in case st' of
             Empty ->
                 let ary' = A.delete ary i
                     bm   = fullBitmap .&. complement (1 `unsafeShiftL` i)
                 in BitmapIndexed bm ary'
             _ -> Full (A.update ary i st')
-      where i = index' shiftedHash
+      where i = indexSH shiftedHash
     go collPos _shiftedHash _k (Collision h v)
       | A.length v == 2
       = if collPos == 0
@@ -1214,20 +1208,6 @@ deleteKeyExists !collPos0 !h0 !k0 !m0 = go collPos0 h0 k0 m0
         else Leaf h (A.index v 0)
       | otherwise = Collision h (A.delete v collPos)
     go !_ !_ !_ Empty = Empty -- error "Internal error: deleteKeyExists empty"
-
-    -- Customized version of 'index' that doesn't require a 'Shift'.
-    index' :: Hash -> Int
-    index' w = fromIntegral $ w .&. subkeyMask
-    {-# INLINE index' #-}
-
-    -- Customized version of 'mask' that doesn't require a 'Shift'.
-    mask' :: Word -> Bitmap
-    mask' w = 1 `unsafeShiftL` index' w
-    {-# INLINE mask' #-}
-
-    shiftHash h = h `unsafeShiftR` bitsPerSubkey
-    {-# INLINE shiftHash #-}
-
 {-# NOINLINE deleteKeyExists #-}
 
 -- | \(O(\log n)\) Adjust the value tied to a given key in this map only
@@ -1610,16 +1590,16 @@ unionWithKey f = go 0
         | h1 == h2  = if k1 == k2
                       then Leaf h1 (L k1 (f k1 v1 v2))
                       else collision h1 l1 l2
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (two' s h1 t1 h2 t2)
     go s t1@(Leaf h1 (L k1 v1)) t2@(Collision h2 ls2)
         | h1 == h2  = Collision h1 (updateOrSnocWithKey (\k a b -> (# f k a b #)) k1 v1 ls2)
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (two' s h1 t1 h2 t2)
     go s t1@(Collision h1 ls1) t2@(Leaf h2 (L k2 v2))
         | h1 == h2  = Collision h1 (updateOrSnocWithKey (\k a b -> (# f k b a #)) k2 v2 ls1)
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (two' s h1 t1 h2 t2)
     go s t1@(Collision h1 ls1) t2@(Collision h2 ls2)
         | h1 == h2  = Collision h1 (updateOrConcatWithKey (\k a b -> (# f k a b #)) ls1 ls2)
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (two' s h1 t1 h2 t2)
     -- branch vs. branch
     go s (BitmapIndexed b1 ary1) (BitmapIndexed b2 ary2) =
         let b'   = b1 .|. b2
@@ -1672,14 +1652,6 @@ unionWithKey f = go 0
     leafHashCode (Leaf h _) = h
     leafHashCode (Collision h _) = h
     leafHashCode _ = error "leafHashCode"
-
-    goDifferentHash s h1 h2 t1 t2
-        | m1 == m2  = BitmapIndexed m1 (A.singleton $! goDifferentHash (nextShift s) h1 h2 t1 t2)
-        | m1 <  m2  = BitmapIndexed (m1 .|. m2) (A.pair t1 t2)
-        | otherwise = BitmapIndexed (m1 .|. m2) (A.pair t2 t1)
-      where
-        m1 = mask h1 s
-        m2 = mask h2 s
 {-# INLINE unionWithKey #-}
 
 -- | Strict in the result of @f@.
@@ -2510,6 +2482,34 @@ nextShift :: Shift -> Shift
 nextShift s = s + bitsPerSubkey
 {-# INLINE nextShift #-}
 
+------------------------------------------------------------------------
+-- ShiftedHash
+
+-- | Sometimes it's more efficient to right-shift the hashes directly instead
+-- of keeping track of an additional 'Shift' value.
+type ShiftedHash = Hash
+
+-- | Construct a 'ShiftedHash' from a 'Shift' and a 'Hash'.
+shiftHash :: Shift -> Hash -> ShiftedHash
+shiftHash s h = h `unsafeShiftR` s
+{-# INLINE shiftHash #-}
+
+-- | Update a 'ShiftedHash' for the next level of the tree.
+nextSH :: ShiftedHash -> ShiftedHash
+nextSH sh = sh `unsafeShiftR` bitsPerSubkey
+{-# INLINE nextSH #-}
+
+-- | Version of 'index' for use with @'ShiftedHash'es@.
+indexSH :: ShiftedHash -> Int
+indexSH sh = fromIntegral $ sh .&. subkeyMask
+{-# INLINE indexSH #-}
+
+-- | Version of 'mask' for use with @'ShiftedHash'es@.
+maskSH :: ShiftedHash -> Bitmap
+maskSH sh = 1 `unsafeShiftL` indexSH sh
+{-# INLINE maskSH #-}
+
+
 ------------------------------------------------------------------------
 -- Pointer equality
 
diff --git a/Data/HashMap/Internal/Strict.hs b/Data/HashMap/Internal/Strict.hs
index ce9a48fa..1c064ab1 100644
--- a/Data/HashMap/Internal/Strict.hs
+++ b/Data/HashMap/Internal/Strict.hs
@@ -216,7 +216,7 @@ insertWith f k0 v0 m0 = go h0 k0 v0 0 m0
       where i = index h s
     go h k x s t@(Collision hy v)
         | h == hy   = Collision h (updateOrSnocWith f k x v)
-        | otherwise = go h k x s $ BitmapIndexed (mask hy s) (A.singleton t)
+        | otherwise = x `seq` runST (HM.two s h k x hy t)
 {-# INLINABLE insertWith #-}
 
 -- | In-place update version of insertWith
@@ -257,7 +257,7 @@ unsafeInsertWithKey f k0 v0 m0 = runST (go h0 k0 v0 0 m0)
       where i = index h s
     go h k x s t@(Collision hy v)
         | h == hy   = return $! Collision h (updateOrSnocWithKey f k x v)
-        | otherwise = go h k x s $ BitmapIndexed (mask hy s) (A.singleton t)
+        | otherwise = x `seq` HM.two s h k x hy t
 {-# INLINABLE unsafeInsertWithKey #-}
 
 -- | \(O(\log n)\) Adjust the value tied to a given key in this map only
@@ -465,16 +465,16 @@ unionWithKey f = go 0
         | h1 == h2  = if k1 == k2
                       then leaf h1 k1 (f k1 v1 v2)
                       else HM.collision h1 l1 l2
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (HM.two' s h1 t1 h2 t2)
     go s t1@(Leaf h1 (L k1 v1)) t2@(Collision h2 ls2)
         | h1 == h2  = Collision h1 (updateOrSnocWithKey f k1 v1 ls2)
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (HM.two' s h1 t1 h2 t2)
     go s t1@(Collision h1 ls1) t2@(Leaf h2 (L k2 v2))
         | h1 == h2  = Collision h1 (updateOrSnocWithKey (flip . f) k2 v2 ls1)
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (HM.two' s h1 t1 h2 t2)
     go s t1@(Collision h1 ls1) t2@(Collision h2 ls2)
         | h1 == h2  = Collision h1 (HM.updateOrConcatWithKey (\k a b -> let !v = f k a b in (# v #)) ls1 ls2)
-        | otherwise = goDifferentHash s h1 h2 t1 t2
+        | otherwise = runST (HM.two' s h1 t1 h2 t2)
     -- branch vs. branch
     go s (BitmapIndexed b1 ary1) (BitmapIndexed b2 ary2) =
         let b'   = b1 .|. b2
@@ -527,14 +527,6 @@ unionWithKey f = go 0
     leafHashCode (Leaf h _) = h
     leafHashCode (Collision h _) = h
     leafHashCode _ = error "leafHashCode"
-
-    goDifferentHash s h1 h2 t1 t2
-        | m1 == m2  = BitmapIndexed m1 (A.singleton $! goDifferentHash (nextShift s) h1 h2 t1 t2)
-        | m1 <  m2  = BitmapIndexed (m1 .|. m2) (A.pair t1 t2)
-        | otherwise = BitmapIndexed (m1 .|. m2) (A.pair t2 t1)
-      where
-        m1 = mask h1 s
-        m2 = mask h2 s
 {-# INLINE unionWithKey #-}
 
 ------------------------------------------------------------------------