diff --git a/Data/HashMap/Internal.hs b/Data/HashMap/Internal.hs
index e5b732cd..41f0d738 100644
--- a/Data/HashMap/Internal.hs
+++ b/Data/HashMap/Internal.hs
@@ -163,6 +163,7 @@ import Data.Functor.Identity      (Identity (..))
 import Data.Hashable              (Hashable)
 import Data.Hashable.Lifted       (Hashable1, Hashable2)
 import Data.HashMap.Internal.List (isPermutationBy, unorderedCompare)
+import Data.Maybe                 (isNothing)
 import Data.Semigroup             (Semigroup (..), stimesIdempotentMonoid)
 import GHC.Exts                   (Int (..), Int#, TYPE, (==#))
 import GHC.Stack                  (HasCallStack)
@@ -1102,56 +1103,60 @@ delete k m = delete' (hash k) k m
 {-# INLINABLE delete #-}
 
 delete' :: Eq k => Hash -> k -> HashMap k v -> HashMap k v
-delete' h0 k0 m0 = go h0 k0 0 m0
-  where
-    go !_ !_ !_ Empty = Empty
-    go h k _ t@(Leaf hy (L ky _))
-        | hy == h && ky == k = Empty
-        | otherwise          = t
-    go h k s t@(BitmapIndexed b ary)
-        | b .&. m == 0 = t
-        | otherwise =
-            let !st = A.index ary i
-                !st' = go h k (nextShift s) st
-            in if st' `ptrEq` st
-                then t
-                else case st' of
-                Empty | A.length ary == 1 -> Empty
-                      | A.length ary == 2 ->
-                          case (i, A.index ary 0, A.index ary 1) of
-                          (0, _, l) | isLeafOrCollision l -> l
-                          (1, l, _) | isLeafOrCollision l -> l
-                          _                               -> bIndexed
-                      | otherwise -> bIndexed
-                    where
-                      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 h s
-            i = sparseIndex b m
-    go h k s t@(Full ary) =
-        let !st   = A.index ary i
-            !st' = go h k (nextShift s) st
+delete' h0 k0 m0 = deleteSubTree h0 k0 0 m0
+{-# INLINABLE delete' #-}
+
+-- | This version of 'delete' can be used on subtrees when a the
+-- corresponding 'Shift' argument is supplied.
+deleteSubTree :: Eq k => Hash -> k -> Shift -> HashMap k v -> HashMap k v
+deleteSubTree !_ !_ !_ Empty = Empty
+deleteSubTree h k _ t@(Leaf hy (L ky _))
+    | hy == h && ky == k = Empty
+    | otherwise          = t
+deleteSubTree h k s t@(BitmapIndexed b ary)
+    | b .&. m == 0 = t
+    | otherwise =
+        let !st = A.index ary i
+            !st' = deleteSubTree h k (nextShift s) st
         in if st' `ptrEq` st
             then t
             else 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 h s
-    go h k _ t@(Collision hy v)
-        | h == hy = case indexOf k v of
-            Just i
-                | A.length v == 2 ->
-                    if i == 0
-                    then Leaf h (A.index v 1)
-                    else Leaf h (A.index v 0)
-                | otherwise -> Collision h (A.delete v i)
-            Nothing -> t
-        | otherwise = t
-{-# INLINABLE delete' #-}
+            Empty | A.length ary == 1 -> Empty
+                  | A.length ary == 2 ->
+                      case (i, A.index ary 0, A.index ary 1) of
+                      (0, _, l) | isLeafOrCollision l -> l
+                      (1, l, _) | isLeafOrCollision l -> l
+                      _                               -> bIndexed
+                  | otherwise -> bIndexed
+                where
+                  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 h s
+        i = sparseIndex b m
+deleteSubTree h k s t@(Full ary) =
+    let !st   = A.index ary i
+        !st' = deleteSubTree h k (nextShift s) st
+    in if st' `ptrEq` st
+        then t
+        else case st' of
+        Empty ->
+            let ary' = A.delete ary i
+                bm   = fullBitmap .&. complement (1 `unsafeShiftL` i)
+            in BitmapIndexed bm ary'
+        _ -> Full (updateFullArray ary i st')
+  where i = index h s
+deleteSubTree h k _ t@(Collision hy v)
+    | h == hy = case indexOf k v of
+        Just i
+            | A.length v == 2 ->
+                if i == 0
+                then Leaf h (A.index v 1)
+                else Leaf h (A.index v 0)
+            | otherwise -> Collision h (A.delete v i)
+        Nothing -> t
+    | otherwise = t
+{-# INLINABLE deleteSubTree #-}
 
 -- | Delete optimized for the case when we know the key is in the map.
 --
@@ -1188,7 +1193,7 @@ deleteKeyExists !collPos0 !h0 !k0 !m0 = go collPos0 h0 k0 m0
                 let ary' = A.delete ary i
                     bm   = fullBitmap .&. complement (1 `unsafeShiftL` i)
                 in BitmapIndexed bm ary'
-            _ -> Full (A.update ary i st')
+            _ -> Full (updateFullArray ary i st')
       where i = indexSH shiftedHash
     go collPos _shiftedHash _k (Collision h v)
       | A.length v == 2
@@ -1780,14 +1785,150 @@ mapKeys f = fromList . foldrWithKey (\k x xs -> (f k, x) : xs) []
 
 -- | \(O(n \log m)\) Difference of two maps. Return elements of the first map
 -- not existing in the second.
-difference :: (Eq k, Hashable k) => HashMap k v -> HashMap k w -> HashMap k v
-difference a b = foldlWithKey' go empty a
+difference :: Eq k => HashMap k v -> HashMap k w -> HashMap k v
+difference = go 0
   where
-    go m k v = case lookup k b of
-                 Nothing -> unsafeInsert k v m
-                 _       -> m
+{- Somehow we get repeated "cases of" on the Hashmap arguments:
+
+        $wgo1
+          = \ (ww :: Int#) (ds :: HashMap k v) (ds1 :: HashMap k w) ->
+              case ds of wild {
+                __DEFAULT ->
+                  case ds1 of wild1 {
+                    __DEFAULT ->
+                      case wild of wild2 {
+                        BitmapIndexed bx bx1 ->
+                          case wild1 of {
+                            BitmapIndexed bx2 bx3 ->
+
+Maybe don't force the first !_?!
+
+Or maybe this helps avoid more evaluations later on? (Check Cmm)
+-}
+    go !_s Empty !_ = Empty
+    go s t1@(Leaf h1 (L k1 _)) t2
+      = lookupCont (\_ -> t1) (\_ _ -> Empty) h1 k1 s t2
+    go _ t1 Empty = t1
+    go s t1 (Leaf h2 (L k2 _)) = deleteSubTree h2 k2 s t1
+
+    go s t1@(BitmapIndexed b1 ary1) (BitmapIndexed b2 ary2)
+      = differenceArrays go s b1 ary1 t1 b2 ary2
+    go s t1@(Full ary1) (BitmapIndexed b2 ary2)
+      = differenceArrays go s fullBitmap ary1 t1 b2 ary2
+    go s t1@(BitmapIndexed b1 ary1) (Full ary2)
+      = differenceArrays go s b1 ary1 t1 fullBitmap ary2
+    go s t1@(Full ary1) (Full ary2)
+      = differenceArrays go s fullBitmap ary1 t1 fullBitmap ary2
+
+    go s t1@(Collision h1 _) (BitmapIndexed b2 ary2)
+        | b2 .&. m == 0 = t1
+        | otherwise = go (nextShift s) t1 (A.index ary2 (sparseIndex b2 m))
+      where m = mask h1 s
+    go s t1@(Collision h1 _) (Full ary2)
+      = go (nextShift s) t1 (A.index ary2 (index h1 s))
+
+    go s t1@(BitmapIndexed b1 ary1) t2@(Collision h2 _)
+        | b1 .&. m == 0 = t1
+        | otherwise =
+            let !st = A.index ary1 i1
+            in case go (nextShift s) st t2 of
+              Empty {- | A.length ary1 == 1 -> Empty -- Impossible! -}
+                    | A.length ary1 == 2 ->
+                        case (i1, A.index ary1 0, A.index ary1 1) of
+                        (0, _, l) | isLeafOrCollision l -> l
+                        (1, l, _) | isLeafOrCollision l -> l
+                        _                               -> bIndexed
+                    | otherwise -> bIndexed
+                  where
+                    bIndexed = BitmapIndexed (b1 .&. complement m) (A.delete ary1 i1)
+              st' | isLeafOrCollision st' && A.length ary1 == 1 -> st'
+                  | st `ptrEq` st' -> t1
+                  | otherwise -> BitmapIndexed b1 (A.update ary1 i1 st')
+      where
+        m = mask h2 s
+        i1 = sparseIndex b1 m
+    go s t1@(Full ary1) t2@(Collision h2 _)
+      = let !st = A.index ary1 i
+        in case go (nextShift s) st t2 of
+          Empty ->
+              let ary1' = A.delete ary1 i
+                  bm   = fullBitmap .&. complement (1 `unsafeShiftL` i)
+              in BitmapIndexed bm ary1'
+          st' | st `ptrEq` st' -> t1
+              | otherwise -> Full (updateFullArray ary1 i st')
+      where i = index h2 s
+
+    -- TODO: Why does $wdifferenceCollisions appear three times in the Core
+    -- for difference, and not just once?
+    go _ t1@(Collision h1 ary1) (Collision h2 ary2)
+      = differenceCollisions h1 ary1 t1 h2 ary2
 {-# INLINABLE difference #-}
 
+differenceArrays :: (Shift -> HashMap k1 v1 -> HashMap k1 v2 -> HashMap k1 v1) -> Shift -> Bitmap -> A.Array (HashMap k1 v1) -> HashMap k1 v1 -> Bitmap -> A.Array (HashMap k1 v2) -> HashMap k1 v1
+differenceArrays diff !s !b1 !ary1 !t1 !b2 !ary2
+  | b1 .&. b2 == 0 = t1
+  | {- b1 == b2 && -} A.unsafeSameArray ary1 ary2 = Empty
+  | otherwise = runST $ do
+    mary <- A.new_ $ A.length ary1
+
+    -- TODO: i == popCount bResult. Not sure if that would be faster.
+    -- Also i1 is in some relation with b1'
+    --
+    -- TODO: Depending on sameAs1 the Core contains jumps to either
+    -- $s$wgo or $s$wgo1. Maybe it would be better to keep track of
+    -- the "sameness" as an Int?!
+    let go !i !i1 !b1' !bResult !sameAs1
+          | b1' == 0 = pure (bResult, sameAs1)
+          | otherwise = do
+            !st1 <- A.indexM ary1 i1
+            case m .&. b2 of
+              0 -> do
+                A.write mary i st1
+                go (i + 1) (i1 + 1) nextB1' (bResult .|. m) sameAs1
+              _ -> do
+                !st2 <- A.indexM ary2 (sparseIndex b2 m)
+                case diff (nextShift s) st1 st2 of
+                  Empty -> go i (i1 + 1) nextB1' bResult False
+                  st -> do
+                    A.write mary i st
+                    let same = st `ptrEq` st1
+                    go (i + 1) (i1 + 1) nextB1' (bResult .|. m) (sameAs1 && same)
+          where
+            m = b1' .&. negate b1'
+            nextB1' = b1' .&. complement m
+
+    (bResult, sameAs1) <- go 0 0 b1 0 True -- FIXME: Does this allocate a tuple?
+    if sameAs1
+      then pure t1
+      else case popCount bResult of
+        0 -> pure Empty
+        1 -> do
+          l <- A.read mary 0
+          if isLeafOrCollision l
+            then pure l
+            else BitmapIndexed bResult <$> (A.unsafeFreeze =<< A.shrink mary 1)
+        n -> bitmapIndexedOrFull bResult <$> (A.unsafeFreeze =<< A.shrink mary n)
+{-# INLINABLE differenceArrays #-}
+
+-- TODO: This could be faster if we would keep track of which elements of ary2
+-- we've already matched. Those could be skipped when we check the following
+-- elements of ary1.
+--
+-- TODO: Get ary1 unboxed somehow?! The reboxing is quite weird.
+-- Maybe try a different order of arguments?!
+differenceCollisions :: Eq k => Hash -> A.Array (Leaf k v1) -> HashMap k v1 -> Hash -> A.Array (Leaf k v2) -> HashMap k v1
+differenceCollisions !h1 !ary1 t1 !h2 !ary2
+  | h1 == h2 =
+    -- TODO: This actually allocates Maybes!
+    let ary = A.filter (\(L k1 _) -> isNothing (indexOf k1 ary2)) ary1
+    in case A.length ary of
+      0 -> Empty
+      1 -> Leaf h1 (A.index ary 0)
+      n | A.length ary1 == n -> t1
+        | otherwise -> Collision h1 ary
+  | otherwise = t1
+{-# INLINABLE differenceCollisions #-}
+
 -- | \(O(n \log m)\) Difference with a combining function. When two equal keys are
 -- encountered, the combining function is applied to the values of these keys.
 -- If it returns 'Nothing', the element is discarded (proper set difference). If
diff --git a/Data/HashMap/Internal/Array.hs b/Data/HashMap/Internal/Array.hs
index 3e47b0c4..2c023638 100644
--- a/Data/HashMap/Internal/Array.hs
+++ b/Data/HashMap/Internal/Array.hs
@@ -72,6 +72,7 @@ module Data.HashMap.Internal.Array
     , thaw
     , map
     , map'
+    , filter
     , traverse
     , traverse'
     , toList
@@ -113,12 +114,14 @@ import qualified Prelude
 if (_k_) < 0 || (_k_) >= (_len_) then error ("Data.HashMap.Internal.Array." ++ (_func_) ++ ": bounds error, offset " ++ show (_k_) ++ ", length " ++ show (_len_)) else
 # define CHECK_OP(_func_,_op_,_lhs_,_rhs_) \
 if not ((_lhs_) _op_ (_rhs_)) then error ("Data.HashMap.Internal.Array." ++ (_func_) ++ ": Check failed: _lhs_ _op_ _rhs_ (" ++ show (_lhs_) ++ " vs. " ++ show (_rhs_) ++ ")") else
+# define CHECK_GE(_func_,_lhs_,_rhs_) CHECK_OP(_func_,>=,_lhs_,_rhs_)
 # define CHECK_GT(_func_,_lhs_,_rhs_) CHECK_OP(_func_,>,_lhs_,_rhs_)
 # define CHECK_LE(_func_,_lhs_,_rhs_) CHECK_OP(_func_,<=,_lhs_,_rhs_)
 # define CHECK_EQ(_func_,_lhs_,_rhs_) CHECK_OP(_func_,==,_lhs_,_rhs_)
 #else
 # define CHECK_BOUNDS(_func_,_len_,_k_)
 # define CHECK_OP(_func_,_op_,_lhs_,_rhs_)
+# define CHECK_GE(_func_,_lhs_,_rhs_)
 # define CHECK_GT(_func_,_lhs_,_rhs_)
 # define CHECK_LE(_func_,_lhs_,_rhs_)
 # define CHECK_EQ(_func_,_lhs_,_rhs_)
@@ -221,7 +224,7 @@ new_ n = new n undefinedElem
 -- | The returned array is the same as the array given, as it is shrunk in place.
 shrink :: MArray s a -> Int -> ST s (MArray s a)
 shrink mary _n@(I# n#) =
-  CHECK_GT("shrink", _n, (0 :: Int))
+  CHECK_GE("shrink", _n, (0 :: Int))
   CHECK_LE("shrink", _n, (unsafeLengthM mary))
   ST $ \s -> case Exts.shrinkSmallMutableArray# (unMArray mary) n# s of
     s' -> (# s', mary #)
@@ -496,6 +499,25 @@ map' f = \ ary ->
              go ary mary (i+1) n
 {-# INLINE map' #-}
 
+filter :: (a -> Bool) -> Array a -> Array a
+filter f = \ ary ->
+    let !n = length ary
+    in run $ do
+      mary <- new_ n
+      len <- go ary mary 0 0 n
+      shrink mary len
+  where
+    go ary mary iAry iMary n
+      | iAry >= n = return iMary
+      | otherwise = do
+        x <- indexM ary iAry
+        if f x
+          then do
+            write mary iMary x
+            go ary mary (iAry + 1) (iMary + 1) n
+          else go ary mary (iAry + 1) iMary n
+{-# INLINE filter #-}
+
 fromList :: Int -> [a] -> Array a
 fromList n xs0 =
     CHECK_EQ("fromList", n, Prelude.length xs0)