diff --git a/Data/HashMap/Internal.hs b/Data/HashMap/Internal.hs
index c5912a7a..49808824 100644
--- a/Data/HashMap/Internal.hs
+++ b/Data/HashMap/Internal.hs
@@ -78,6 +78,7 @@ module Data.HashMap.Internal
     , intersection
     , intersectionWith
     , intersectionWithKey
+    , intersectionWithKey#
 
       -- * Folds
     , foldr'
@@ -150,9 +151,9 @@ import Data.Data                  (Constr, Data (..), DataType)
 import Data.Functor.Classes       (Eq1 (..), Eq2 (..), Ord1 (..), Ord2 (..),
                                    Read1 (..), Show1 (..), Show2 (..))
 import Data.Functor.Identity      (Identity (..))
-import Data.HashMap.Internal.List (isPermutationBy, unorderedCompare)
 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.Stack                  (HasCallStack)
@@ -163,9 +164,9 @@ import Text.Read                  hiding (step)
 import qualified Data.Data                   as Data
 import qualified Data.Foldable               as Foldable
 import qualified Data.Functor.Classes        as FC
-import qualified Data.HashMap.Internal.Array as A
 import qualified Data.Hashable               as H
 import qualified Data.Hashable.Lifted        as H
+import qualified Data.HashMap.Internal.Array as A
 import qualified Data.List                   as List
 import qualified GHC.Exts                    as Exts
 import qualified Language.Haskell.TH.Syntax  as TH
@@ -1627,7 +1628,7 @@ unionArrayBy f !b1 !b2 !ary1 !ary2 = A.run $ do
                 A.write mary i =<< A.indexM ary2 i2
                 go (i+1) i1 (i2+1) b'
           where
-            m = 1 `unsafeShiftL` (countTrailingZeros b)
+            m = 1 `unsafeShiftL` countTrailingZeros b
             testBit x = x .&. m /= 0
             b' = b .&. complement m
     go 0 0 0 bCombined
@@ -1759,37 +1760,161 @@ differenceWith f a b = foldlWithKey' go empty a
 -- | \(O(n \log m)\) Intersection of two maps. Return elements of the first
 -- map for keys existing in the second.
 intersection :: (Eq k, Hashable k) => HashMap k v -> HashMap k w -> HashMap k v
-intersection a b = foldlWithKey' go empty a
-  where
-    go m k v = case lookup k b of
-                 Just _ -> unsafeInsert k v m
-                 _      -> m
+intersection = Exts.inline intersectionWith const
 {-# INLINABLE intersection #-}
 
 -- | \(O(n \log m)\) Intersection of two maps. If a key occurs in both maps
 -- the provided function is used to combine the values from the two
 -- maps.
-intersectionWith :: (Eq k, Hashable k) => (v1 -> v2 -> v3) -> HashMap k v1
-                 -> HashMap k v2 -> HashMap k v3
-intersectionWith f a b = foldlWithKey' go empty a
-  where
-    go m k v = case lookup k b of
-                 Just w -> unsafeInsert k (f v w) m
-                 _      -> m
+intersectionWith :: (Eq k, Hashable k) => (v1 -> v2 -> v3) -> HashMap k v1 -> HashMap k v2 -> HashMap k v3
+intersectionWith f = Exts.inline intersectionWithKey $ const f
 {-# INLINABLE intersectionWith #-}
 
 -- | \(O(n \log m)\) Intersection of two maps. If a key occurs in both maps
 -- the provided function is used to combine the values from the two
 -- maps.
-intersectionWithKey :: (Eq k, Hashable k) => (k -> v1 -> v2 -> v3)
-                    -> HashMap k v1 -> HashMap k v2 -> HashMap k v3
-intersectionWithKey f a b = foldlWithKey' go empty a
-  where
-    go m k v = case lookup k b of
-                 Just w -> unsafeInsert k (f k v w) m
-                 _      -> m
+intersectionWithKey :: (Eq k, Hashable k) => (k -> v1 -> v2 -> v3) -> HashMap k v1 -> HashMap k v2 -> HashMap k v3
+intersectionWithKey f = intersectionWithKey# $ \k v1 v2 -> (# f k v1 v2 #)
 {-# INLINABLE intersectionWithKey #-}
 
+intersectionWithKey# :: Eq k => (k -> v1 -> v2 -> (# v3 #)) -> HashMap k v1 -> HashMap k v2 -> HashMap k v3
+intersectionWithKey# f = go 0
+  where
+    -- empty vs. anything
+    go !_ _ Empty = Empty
+    go _ Empty _ = Empty
+    -- leaf vs. anything
+    go s (Leaf h1 (L k1 v1)) t2 =
+      lookupCont
+        (\_ -> Empty)
+        (\v _ -> case f k1 v1 v of (# v' #) -> Leaf h1 $ L k1 v')
+        h1 k1 s t2
+    go s t1 (Leaf h2 (L k2 v2)) =
+      lookupCont
+        (\_ -> Empty)
+        (\v _ -> case f k2 v v2 of (# v' #) -> Leaf h2 $ L k2 v')
+        h2 k2 s t1
+    -- collision vs. collision
+    go _ (Collision h1 ls1) (Collision h2 ls2) = intersectionCollisions f h1 h2 ls1 ls2
+    -- branch vs. branch
+    go s (BitmapIndexed b1 ary1) (BitmapIndexed b2 ary2) =
+      intersectionArrayBy (go (s + bitsPerSubkey)) b1 b2 ary1 ary2
+    go s (BitmapIndexed b1 ary1) (Full ary2) =
+      intersectionArrayBy (go (s + bitsPerSubkey)) b1 fullNodeMask ary1 ary2
+    go s (Full ary1) (BitmapIndexed b2 ary2) =
+      intersectionArrayBy (go (s + bitsPerSubkey)) fullNodeMask b2 ary1 ary2
+    go s (Full ary1) (Full ary2) =
+      intersectionArrayBy (go (s + bitsPerSubkey)) fullNodeMask fullNodeMask ary1 ary2
+    -- collision vs. branch
+    go s (BitmapIndexed b1 ary1) t2@(Collision h2 _ls2)
+      | b1 .&. m2 == 0 = Empty
+      | otherwise = go (s + bitsPerSubkey) (A.index ary1 i) t2
+      where
+        m2 = mask h2 s
+        i = sparseIndex b1 m2
+    go s t1@(Collision h1 _ls1) (BitmapIndexed b2 ary2)
+      | b2 .&. m1 == 0 = Empty
+      | otherwise = go (s + bitsPerSubkey) t1 (A.index ary2 i)
+      where
+        m1 = mask h1 s
+        i = sparseIndex b2 m1
+    go s (Full ary1) t2@(Collision h2 _ls2) = go (s + bitsPerSubkey) (A.index ary1 i) t2
+      where
+        i = index h2 s
+    go s t1@(Collision h1 _ls1) (Full ary2) = go (s + bitsPerSubkey) t1 (A.index ary2 i)
+      where
+        i = index h1 s
+{-# INLINE intersectionWithKey# #-}
+
+intersectionArrayBy ::
+  ( HashMap k v1 ->
+    HashMap k v2 ->
+    HashMap k v3
+  ) ->
+  Bitmap ->
+  Bitmap ->
+  A.Array (HashMap k v1) ->
+  A.Array (HashMap k v2) ->
+  HashMap k v3
+intersectionArrayBy f !b1 !b2 !ary1 !ary2
+  | b1 .&. b2 == 0 = Empty
+  | otherwise = runST $ do
+    mary <- A.new_ $ popCount bIntersect
+    -- iterate over nonzero bits of b1 .|. b2
+    let go !i !i1 !i2 !b !bFinal
+          | b == 0 = pure (i, bFinal)
+          | testBit $ b1 .&. b2 = do
+            x1 <- A.indexM ary1 i1
+            x2 <- A.indexM ary2 i2
+            case f x1 x2 of
+              Empty -> go i (i1 + 1) (i2 + 1) b' (bFinal .&. complement m)
+              _ -> do
+                A.write mary i $! f x1 x2
+                go (i + 1) (i1 + 1) (i2 + 1) b' bFinal
+          | testBit b1 = go i (i1 + 1) i2 b' bFinal
+          | otherwise = go i i1 (i2 + 1) b' bFinal
+          where
+            m = 1 `unsafeShiftL` countTrailingZeros b
+            testBit x = x .&. m /= 0
+            b' = b .&. complement m
+    (len, bFinal) <- go 0 0 0 bCombined bIntersect
+    case len of
+      0 -> pure Empty
+      1 -> A.read mary 0
+      _ -> bitmapIndexedOrFull bFinal <$> (A.unsafeFreeze =<< A.shrink mary len)
+  where
+    bCombined = b1 .|. b2
+    bIntersect = b1 .&. b2
+{-# INLINE intersectionArrayBy #-}
+
+intersectionCollisions :: Eq k => (k -> v1 -> v2 -> (# v3 #)) -> Hash -> Hash -> A.Array (Leaf k v1) -> A.Array (Leaf k v2) -> HashMap k v3
+intersectionCollisions f h1 h2 ary1 ary2
+  | h1 == h2 = runST $ do
+    mary2 <- A.thaw ary2 0 $ A.length ary2
+    mary <- A.new_ $ min (A.length ary1) (A.length ary2)
+    let go i j
+          | i >= A.length ary1 || j >= A.lengthM mary2 = pure j
+          | otherwise = do
+            L k1 v1 <- A.indexM ary1 i
+            searchSwap k1 j mary2 >>= \case
+              Just (L _k2 v2) -> do
+                let !(# v3 #) = f k1 v1 v2
+                A.write mary j $ L k1 v3
+                go (i + 1) (j + 1)
+              Nothing -> do
+                go (i + 1) j
+    len <- go 0 0
+    case len of
+      0 -> pure Empty
+      1 -> Leaf h1 <$> A.read mary 0
+      _ -> Collision h1 <$> (A.unsafeFreeze =<< A.shrink mary len)
+  | otherwise = Empty
+{-# INLINE intersectionCollisions #-}
+
+-- | Say we have
+-- @
+-- 1 2 3 4
+-- @
+-- and we search for @3@. Then we can mutate the array to
+-- @
+-- undefined 2 1 4
+-- @
+-- We don't actually need to write undefined, we just have to make sure that the next search starts 1 after the current one.
+searchSwap :: Eq k => k -> Int -> A.MArray s (Leaf k v) -> ST s (Maybe (Leaf k v))
+searchSwap toFind start = go start toFind start
+  where
+    go i0 k i mary
+      | i >= A.lengthM mary = pure Nothing
+      | otherwise = do
+        l@(L k' _v) <- A.read mary i
+        if k == k'
+          then do
+            A.write mary i =<< A.read mary i0
+            pure $ Just l
+          else go i0 k (i + 1) mary
+{-# INLINE searchSwap #-}
+
+
 ------------------------------------------------------------------------
 -- * Folds
 
diff --git a/Data/HashMap/Internal/Array.hs b/Data/HashMap/Internal/Array.hs
index 83a927a6..f7696a26 100644
--- a/Data/HashMap/Internal/Array.hs
+++ b/Data/HashMap/Internal/Array.hs
@@ -77,6 +77,7 @@ module Data.HashMap.Internal.Array
     , toList
     , fromList
     , fromList'
+    , shrink
     ) where
 
 import Control.Applicative (liftA2)
@@ -92,6 +93,7 @@ import GHC.Exts            (Int (..), SmallArray#, SmallMutableArray#,
                             thawSmallArray#, unsafeCoerce#,
                             unsafeFreezeSmallArray#, unsafeThawSmallArray#,
                             writeSmallArray#)
+import qualified GHC.Exts as Exts
 import GHC.ST              (ST (..))
 import Prelude             hiding (all, filter, foldMap, foldl, foldr, length,
                             map, read, traverse)
@@ -205,6 +207,20 @@ new _n@(I# n#) b =
 new_ :: Int -> ST s (MArray s a)
 new_ n = new n undefinedElem
 
+-- | When 'Exts.shrinkSmallMutableArray#' is available, the returned array is the same as the array given, as it is shrunk in place.
+-- Otherwise a copy is made.
+shrink :: MArray s a -> Int -> ST s (MArray s a)
+#if __GLASGOW_HASKELL__ >= 810
+shrink mary _n@(I# n#) =
+  CHECK_GT("shrink", _n, (0 :: Int))
+  CHECK_LE("shrink", _n, (lengthM mary))
+  ST $ \s -> case Exts.shrinkSmallMutableArray# (unMArray mary) n# s of
+    s' -> (# s', mary #)
+#else
+shrink mary n = cloneM mary 0 n
+#endif 
+{-# INLINE shrink #-}
+
 singleton :: a -> Array a
 singleton x = runST (singletonM x)
 {-# INLINE singleton #-}
diff --git a/Data/HashMap/Internal/Strict.hs b/Data/HashMap/Internal/Strict.hs
index b25266a4..2d8fb374 100644
--- a/Data/HashMap/Internal/Strict.hs
+++ b/Data/HashMap/Internal/Strict.hs
@@ -128,16 +128,17 @@ import Data.Bits             ((.&.), (.|.))
 import Data.Coerce           (coerce)
 import Data.Functor.Identity (Identity (..))
 -- See Note [Imports from Data.HashMap.Internal]
+import Data.Hashable         (Hashable)
 import Data.HashMap.Internal (Hash, HashMap (..), Leaf (..), LookupRes (..),
                               bitsPerSubkey, fullNodeMask, hash, index, mask,
                               ptrEq, sparseIndex)
-import Data.Hashable         (Hashable)
 import Prelude               hiding (lookup, map)
 
 -- See Note [Imports from Data.HashMap.Internal]
 import qualified Data.HashMap.Internal       as HM
 import qualified Data.HashMap.Internal.Array as A
 import qualified Data.List                   as List
+import qualified GHC.Exts                    as Exts
 
 {-
 Note [Imports from Data.HashMap.Internal]
@@ -616,11 +617,7 @@ differenceWith f a b = HM.foldlWithKey' go HM.empty a
 -- maps.
 intersectionWith :: (Eq k, Hashable k) => (v1 -> v2 -> v3) -> HashMap k v1
                  -> HashMap k v2 -> HashMap k v3
-intersectionWith f a b = HM.foldlWithKey' go HM.empty a
-  where
-    go m k v = case HM.lookup k b of
-                 Just w -> let !x = f v w in HM.unsafeInsert k x m
-                 _      -> m
+intersectionWith f = Exts.inline intersectionWithKey $ const f
 {-# INLINABLE intersectionWith #-}
 
 -- | \(O(n+m)\) Intersection of two maps. If a key occurs in both maps
@@ -628,11 +625,7 @@ intersectionWith f a b = HM.foldlWithKey' go HM.empty a
 -- maps.
 intersectionWithKey :: (Eq k, Hashable k) => (k -> v1 -> v2 -> v3)
                     -> HashMap k v1 -> HashMap k v2 -> HashMap k v3
-intersectionWithKey f a b = HM.foldlWithKey' go HM.empty a
-  where
-    go m k v = case HM.lookup k b of
-                 Just w -> let !x = f k v w in HM.unsafeInsert k x m
-                 _      -> m
+intersectionWithKey f = HM.intersectionWithKey# $ \k v1 v2 -> let !v3 = f k v1 v2 in (# v3 #)
 {-# INLINABLE intersectionWithKey #-}
 
 ------------------------------------------------------------------------
diff --git a/benchmarks/Benchmarks.hs b/benchmarks/Benchmarks.hs
index c0f7f550..ae05c422 100644
--- a/benchmarks/Benchmarks.hs
+++ b/benchmarks/Benchmarks.hs
@@ -318,13 +318,17 @@ main = do
             [ bench "Int" $ whnf (HM.union hmi) hmi2
             , bench "ByteString" $ whnf (HM.union hmbs) hmbsSubset
             ]
+          
+          , bgroup "intersection"
+            [ bench "Int" $ whnf (HM.intersection hmi) hmi2
+            , bench "ByteString" $ whnf (HM.intersection hmbs) hmbsSubset
+            ]
 
             -- Transformations
           , bench "map" $ whnf (HM.map (\ v -> v + 1)) hmi
 
             -- * Difference and intersection
           , bench "difference" $ whnf (HM.difference hmi) hmi2
-          , bench "intersection" $ whnf (HM.intersection hmi) hmi2
 
             -- Folds
           , bench "foldl'" $ whnf (HM.foldl' (+) 0) hmi
diff --git a/tests/Properties/HashMapLazy.hs b/tests/Properties/HashMapLazy.hs
index 8b712da3..f25fb42d 100644
--- a/tests/Properties/HashMapLazy.hs
+++ b/tests/Properties/HashMapLazy.hs
@@ -1,6 +1,7 @@
 {-# LANGUAGE CPP                        #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-} -- because of Arbitrary (HashMap k v)
+{-# LANGUAGE BangPatterns #-}
 
 -- | Tests for the 'Data.HashMap.Lazy' module.  We test functions by
 -- comparing them to @Map@ from @containers@.
@@ -42,7 +43,7 @@ import qualified Data.Map.Lazy     as M
 
 -- Key type that generates more hash collisions.
 newtype Key = K { unK :: Int }
-            deriving (Arbitrary, Eq, Ord, Read, Show)
+            deriving (Arbitrary, Eq, Ord, Read, Show, Num)
 
 instance Hashable Key where
     hashWithSalt salt k = hashWithSalt salt (unK k) `mod` 20
@@ -318,8 +319,10 @@ pDifferenceWith xs ys = M.differenceWith f (M.fromList xs) `eq_`
     f x y = if x == 0 then Nothing else Just (x - y)
 
 pIntersection :: [(Key, Int)] -> [(Key, Int)] -> Bool
-pIntersection xs ys = M.intersection (M.fromList xs) `eq_`
-                      HM.intersection (HM.fromList xs) $ ys
+pIntersection xs ys = 
+  M.intersection (M.fromList xs)
+    `eq_` HM.intersection (HM.fromList xs)
+    $ ys
 
 pIntersectionWith :: [(Key, Int)] -> [(Key, Int)] -> Bool
 pIntersectionWith xs ys = M.intersectionWith (-) (M.fromList xs) `eq_`