diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,8 @@
+0.4
+-------
+* `FilterableWithIndex` and `WitherableWithIndex` are now subclasses of the ones from [indexed-traversable](https://hackage.haskell.org/package/indexed-traversable)
+* Removed the orphan instances for `MonoidalMap`
+
 0.3.5
 -------
 
diff --git a/src/Data/Witherable.hs b/src/Data/Witherable.hs
--- a/src/Data/Witherable.hs
+++ b/src/Data/Witherable.hs
@@ -1,10 +1,5 @@
 {-# LANGUAGE Rank2Types #-}
-{-# LANGUAGE CPP, DeriveFunctor, DeriveFoldable, DeriveTraversable, StandaloneDeriving #-}
-{-# LANGUAGE UndecidableInstances, FlexibleContexts, GeneralizedNewtypeDeriving #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE FunctionalDependencies #-}
-{-# LANGUAGE EmptyCase #-}
+{-# LANGUAGE CPP #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Data.Witherable
@@ -16,7 +11,7 @@
 -- Portability :  non-portable
 --
 -----------------------------------------------------------------------------
-module Data.Witherable
+module Data.Witherable {-# DEPRECATED "Use Witherable instead" #-}
   ( Filterable(..)
   , (<$?>)
   , (<&?>)
@@ -43,37 +38,16 @@
   , Peat(..)
   -- * Wrapper
   , WrappedFoldable(..)
-  )
+  ) where
 
-where
-import qualified Control.Lens as Lens
-import Data.Witherable.Class
-import qualified Data.IntMap.Lazy as IM
-import qualified Data.Map.Lazy as M
-import qualified Data.Map.Monoidal as MM
-import qualified Data.Sequence as S
-import qualified Data.Vector as V
-import qualified Data.HashMap.Lazy as HM
-import qualified Data.Set as Set
-import qualified Data.HashSet as HSet
 import Control.Applicative
-import qualified Data.Traversable as T
-import qualified Data.Foldable as F
-import Data.Functor.Compose
-import Data.Functor.Product as P
-import Data.Functor.Sum as Sum
-import Control.Monad.Trans.Identity
-import Data.Hashable
 import Data.Functor.Identity
-import Data.Functor.Reverse (Reverse (..))
-import Control.Applicative.Backwards (Backwards (..))
+import Witherable
+import qualified Data.Set as Set
+import qualified Data.HashSet as HSet
 import Control.Monad.Trans.State.Strict
-import Data.Monoid
-import Data.Orphans ()
-import Data.Proxy
-import Data.Void
-import Data.Coerce (coerce)
-import Prelude hiding (filter)
+import Data.Hashable
+import Data.Coerce
 
 type Filter s t a b = Wither s t a b
 {-# DEPRECATED Filter "Use Wither instead" #-}
@@ -156,57 +130,6 @@
 filterOf w f = runIdentity . filterAOf w (idDot f)
 {-# INLINE filterOf #-}
 
--- | An infix alias for 'mapMaybe'. The name of the operator alludes
--- to '<$>', and has the same fixity.
---
--- @since 0.3.1
-(<$?>) :: Filterable f => (a -> Maybe b) -> f a -> f b
-(<$?>) = mapMaybe
-infixl 4 <$?>
-
--- | Flipped version of '<$?>', the 'Filterable' version of
--- 'Data.Functor.<&>'. It has the same fixity as 'Data.Functor.<&>'.
---
--- @
--- ('<&?>') = 'flip' 'mapMaybe'
--- @
---
--- @since 0.3.1
-(<&?>) :: Filterable f => f a -> (a -> Maybe b) -> f b
-as <&?> f = mapMaybe f as
-infixl 1 <&?>
-
--- | Indexed variant of 'Filterable'.
-class (Lens.FunctorWithIndex i t, Filterable t) => FilterableWithIndex i t | t -> i where
-  imapMaybe :: (i -> a -> Maybe b) -> t a -> t b
-  imapMaybe f = catMaybes . Lens.imap f
-  {-# INLINE imapMaybe #-}
-
-  -- | @'ifilter' f . 'ifilter' g ≡ ifilter (\i -> 'liftA2' ('&&') (f i) (g i))@
-  ifilter :: (i -> a -> Bool) -> t a -> t a
-  ifilter f = imapMaybe $ \i a -> if f i a then Just a else Nothing
-  {-# INLINE ifilter #-}
-
--- | @'forMaybe' = 'flip' 'wither'@
-forMaybe :: (Witherable t, Applicative f) => t a -> (a -> f (Maybe b)) -> f (t b)
-forMaybe = flip wither
-{-# INLINE forMaybe #-}
-
--- | Indexed variant of 'Witherable'.
-class (Lens.TraversableWithIndex i t, Witherable t) => WitherableWithIndex i t | t -> i where
-  -- | Effectful 'imapMaybe'.
-  --
-  -- @'iwither' (\ i -> 'pure' . f i) ≡ 'pure' . 'imapMaybe' f@
-  iwither :: (Applicative f) => (i -> a -> f (Maybe b)) -> t a -> f (t b)
-  iwither f = fmap catMaybes . Lens.itraverse f
-
-  -- | @Monadic variant of 'wither'. This may have more efficient implementation.@
-  iwitherM :: (Monad m) => (i -> a -> m (Maybe b)) -> t a -> m (t b)
-  iwitherM = iwither
-
-  ifilterA :: (Applicative f) => (i -> a -> f Bool) -> t a -> f (t a)
-  ifilterA f = iwither (\i a -> (\b -> if b then Just a else Nothing) <$> f i a)
-
 -- | Remove the duplicate elements through a filter.
 ordNubOf :: Ord a => FilterLike' (State (Set.Set a)) s a -> s -> s
 ordNubOf w t = evalState (w f t) Set.empty
@@ -225,174 +148,3 @@
       then (Nothing, s)
       else (Just a, HSet.insert a s)
 {-# INLINE hashNubOf #-}
-
--- | Removes duplicate elements from a list, keeping only the first
---   occurrence. This is asymptotically faster than using
---   'Data.List.nub' from "Data.List".
-ordNub :: (Witherable t, Ord a) => t a -> t a
-ordNub = ordNubOf witherM
-{-# INLINE ordNub #-}
-
--- | Removes duplicate elements from a list, keeping only the first
---   occurrence. This is usually faster than 'ordNub', especially for
---   things that have a slow comparison (like 'String').
-hashNub :: (Witherable t, Eq a, Hashable a) => t a -> t a
-hashNub = hashNubOf witherM
-{-# INLINE hashNub #-}
-
--- | A default implementation for 'mapMaybe'.
-mapMaybeDefault :: (F.Foldable f, Alternative f) => (a -> Maybe b) -> f a -> f b
-mapMaybeDefault p = F.foldr (\x xs -> case p x of
-    Just a -> pure a <|> xs
-    _ -> xs) empty
-{-# INLINABLE mapMaybeDefault #-}
-
--- | A default implementation for 'imapMaybe'.
-imapMaybeDefault :: (Lens.FoldableWithIndex i f, Alternative f) => (i -> a -> Maybe b) -> f a -> f b
-imapMaybeDefault p = Lens.ifoldr (\i x xs -> case p i x of
-    Just a -> pure a <|> xs
-    _ -> xs) empty
-{-# INLINABLE imapMaybeDefault #-}
-
-newtype WrappedFoldable f a = WrapFilterable {unwrapFoldable :: f a}
-  deriving (Functor, F.Foldable, T.Traversable, Applicative, Alternative)
-
-instance (Lens.FunctorWithIndex i f) => Lens.FunctorWithIndex i (WrappedFoldable f) where
-  imap f = WrapFilterable . Lens.imap f . unwrapFoldable
-
-instance (Lens.FoldableWithIndex i f) => Lens.FoldableWithIndex i (WrappedFoldable f) where
-  ifoldMap f = Lens.ifoldMap f . unwrapFoldable
-
-instance (Lens.TraversableWithIndex i f) => Lens.TraversableWithIndex i (WrappedFoldable f) where
-  itraverse f = fmap WrapFilterable . Lens.itraverse f . unwrapFoldable
-
-instance (F.Foldable f, Alternative f) => Filterable (WrappedFoldable f) where
-    {-#INLINE mapMaybe#-}
-    mapMaybe = mapMaybeDefault
-
-instance (Lens.FunctorWithIndex i f, Lens.FoldableWithIndex i f, Alternative f) => FilterableWithIndex i (WrappedFoldable f) where
-  {-# INLINE imapMaybe #-}
-  imapMaybe = imapMaybeDefault
-
-instance FilterableWithIndex () Maybe
-
-instance WitherableWithIndex () Maybe
-
--- Option doesn't have the necessary instances in Lens
---instance FilterableWithIndex () Option
---instance WitherableWithIndex () Option
-
-instance FilterableWithIndex Int []
-
-instance FilterableWithIndex Int ZipList
-
-instance (Alternative f, T.Traversable f) => Witherable (WrappedFoldable f)
-
-instance WitherableWithIndex Int []
-
-instance WitherableWithIndex Int ZipList
-
-instance FilterableWithIndex Int IM.IntMap where
-  imapMaybe = IM.mapMaybeWithKey
-  ifilter = IM.filterWithKey
-
-instance WitherableWithIndex Int IM.IntMap where
-
-instance FilterableWithIndex k (M.Map k) where
-  imapMaybe = M.mapMaybeWithKey
-  ifilter = M.filterWithKey
-
-instance WitherableWithIndex k (M.Map k) where
-#if MIN_VERSION_containers(0,5,8)
-  iwither = M.traverseMaybeWithKey
-#endif
-
-instance Filterable (MM.MonoidalMap k) where
-  mapMaybe = MM.mapMaybe
-  filter = MM.filter
-
-instance Witherable (MM.MonoidalMap k)
-
-instance FilterableWithIndex k (MM.MonoidalMap k) where
-  imapMaybe = MM.mapMaybeWithKey
-  ifilter = MM.filterWithKey
-
-instance WitherableWithIndex k (MM.MonoidalMap k)
-
-instance (Eq k, Hashable k) => FilterableWithIndex k (HM.HashMap k) where
-  imapMaybe = HM.mapMaybeWithKey
-  ifilter = HM.filterWithKey
-
-instance (Eq k, Hashable k) => WitherableWithIndex k (HM.HashMap k) where
-
-instance FilterableWithIndex Void Proxy
-
-instance WitherableWithIndex Void Proxy
-
-instance FilterableWithIndex Int V.Vector where
-  imapMaybe = V.imapMaybe
-  ifilter = V.ifilter
-
-instance WitherableWithIndex Int V.Vector
-
-instance FilterableWithIndex Int S.Seq
-
-instance WitherableWithIndex Int S.Seq
-
-instance (Lens.FunctorWithIndex i f, FilterableWithIndex j g) => FilterableWithIndex (i, j) (Compose f g) where
-  imapMaybe f = Compose . Lens.imap (\i -> imapMaybe (\j -> f (i, j))) . getCompose
-  ifilter p = Compose . Lens.imap (\i -> ifilter (\j -> p (i, j))) . getCompose
-
-instance (Lens.TraversableWithIndex i f, WitherableWithIndex j g) => WitherableWithIndex (i, j) (Compose f g) where
-  iwither f = fmap Compose . Lens.itraverse (\i -> iwither (\j -> f (i, j))) . getCompose
-  iwitherM f = fmap Compose . Lens.imapM (\i -> iwitherM (\j -> f (i, j))) . getCompose
-  ifilterA p = fmap Compose . Lens.itraverse (\i -> ifilterA (\j -> p (i, j))) . getCompose
-
-instance (FilterableWithIndex i f, FilterableWithIndex j g) => FilterableWithIndex (Either i j) (P.Product f g) where
-  imapMaybe f (P.Pair x y) = P.Pair (imapMaybe (f . Left) x) (imapMaybe (f . Right) y)
-  ifilter p (P.Pair x y) = P.Pair (ifilter (p . Left) x) (ifilter (p . Right) y)
-
-instance (WitherableWithIndex i f, WitherableWithIndex j g) => WitherableWithIndex (Either i j) (P.Product f g) where
-  iwither f (P.Pair x y) = liftA2 P.Pair (iwither (f . Left) x) (iwither (f . Right) y)
-  iwitherM f (P.Pair x y) = liftA2 P.Pair (iwitherM (f . Left) x) (iwitherM (f . Right) y)
-  ifilterA p (P.Pair x y) = liftA2 P.Pair (ifilterA (p . Left) x) (ifilterA (p . Right) y)
-
-instance (FilterableWithIndex i f, FilterableWithIndex j g) => FilterableWithIndex (Either i j) (Sum.Sum f g) where
-  imapMaybe f (Sum.InL x) = Sum.InL (imapMaybe (f . Left) x)
-  imapMaybe f (Sum.InR y) = Sum.InR (imapMaybe (f . Right) y)
-
-  ifilter f (Sum.InL x) = Sum.InL (ifilter (f . Left) x)
-  ifilter f (Sum.InR y) = Sum.InR (ifilter (f . Right) y)
-
-instance (WitherableWithIndex i f, WitherableWithIndex j g) => WitherableWithIndex (Either i j) (Sum.Sum f g) where
-  iwither f (Sum.InL x) = Sum.InL <$> iwither (f . Left) x
-  iwither f (Sum.InR y) = Sum.InR <$> iwither (f . Right) y
-
-  iwitherM f (Sum.InL x) = Sum.InL <$> iwitherM (f . Left) x
-  iwitherM f (Sum.InR y) = Sum.InR <$> iwitherM (f . Right) y
-
-  ifilterA f (Sum.InL x) = Sum.InL <$> ifilterA (f . Left) x
-  ifilterA f (Sum.InR y) = Sum.InR <$> ifilterA (f . Right) y
-
-deriving instance (FilterableWithIndex i f) => FilterableWithIndex i (IdentityT f)
-
-instance (WitherableWithIndex i f) => WitherableWithIndex i (IdentityT f) where
-  iwither f (IdentityT m) = IdentityT <$> iwither f m
-  iwitherM f (IdentityT m) = IdentityT <$> iwitherM f m
-  ifilterA p (IdentityT m) = IdentityT <$> ifilterA p m
-
-deriving instance FilterableWithIndex i t => FilterableWithIndex i (Reverse t)
-
--- | Wither from right to left.
-instance WitherableWithIndex i t => WitherableWithIndex i (Reverse t) where
-  iwither f (Reverse t) = fmap Reverse . forwards $ iwither (\i -> Backwards . f i) t
-  -- We can't do anything special with iwitherM, because Backwards m is not
-  -- generally a Monad.
-  ifilterA p (Reverse t) = fmap Reverse . forwards $ ifilterA (\i -> Backwards . p i) t
-
-deriving instance FilterableWithIndex i t => FilterableWithIndex i (Backwards t)
-
-instance WitherableWithIndex i t => WitherableWithIndex i (Backwards t) where
-  iwither f (Backwards xs) = Backwards <$> iwither f xs
-  iwitherM f (Backwards xs) = Backwards <$> iwitherM f xs
-  ifilterA f (Backwards xs) = Backwards <$> ifilterA f xs
diff --git a/src/Witherable.hs b/src/Witherable.hs
new file mode 100644
--- /dev/null
+++ b/src/Witherable.hs
@@ -0,0 +1,646 @@
+{-# LANGUAGE Rank2Types #-}
+{-# LANGUAGE CPP, DeriveFunctor, DeriveFoldable, DeriveTraversable, StandaloneDeriving #-}
+{-# LANGUAGE UndecidableInstances, FlexibleContexts, GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE FunctionalDependencies #-}
+{-# LANGUAGE EmptyCase #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Witherable
+-- Copyright   :  (c) Fumiaki Kinoshita 2020
+-- License     :  BSD3
+--
+-- Maintainer  :  Fumiaki Kinoshita <fumiexcel@gmail.com>
+-- Stability   :  provisional
+-- Portability :  non-portable
+--
+-----------------------------------------------------------------------------
+module Witherable
+  ( Filterable(..)
+  , (<$?>)
+  , (<&?>)
+  , Witherable(..)
+  , ordNub
+  , hashNub
+  , forMaybe
+  -- * Indexed variants
+  , FilterableWithIndex(..)
+  , WitherableWithIndex(..)
+  -- * Wrapper
+  , WrappedFoldable(..)
+  )
+
+where
+
+import Control.Applicative
+import Control.Applicative.Backwards (Backwards (..))
+import Control.Monad.Trans.Identity
+import Control.Monad.Trans.Maybe
+import Control.Monad.Trans.State.Strict
+import Data.Bool (bool)
+import Data.Coerce (coerce)
+import Data.Foldable.WithIndex
+import Data.Functor.Compose
+import Data.Functor.Product as P
+import Data.Functor.Reverse (Reverse (..))
+import Data.Functor.Sum as Sum
+import Data.Functor.WithIndex
+import Data.Functor.WithIndex.Instances ()
+import Data.Hashable
+import Data.Monoid
+import Data.Orphans ()
+import Data.Proxy
+import Data.Semigroup (Option (..))
+import Data.Traversable.WithIndex
+import Data.Void
+import Prelude hiding (filter)
+import qualified Data.Foldable as F
+import qualified Data.HashMap.Lazy as HM
+import qualified Data.HashSet as HSet
+import qualified Data.IntMap.Lazy as IM
+import qualified Data.Map.Lazy as M
+import qualified Data.Maybe as Maybe
+import qualified Data.Sequence as S
+import qualified Data.Set as Set
+import qualified Data.Traversable as T
+import qualified Data.Vector as V
+import qualified GHC.Generics as Generics
+import qualified Prelude
+
+-- | Like 'Functor', but you can remove elements instead of updating them.
+--
+-- Formally, the class 'Filterable' represents a functor from @Kleisli Maybe@ to @Hask@.
+--
+-- A definition of 'mapMaybe' must satisfy the following laws:
+--
+-- [/conservation/]
+--   @'mapMaybe' (Just . f) ≡ 'fmap' f@
+--
+-- [/composition/]
+--   @'mapMaybe' f . 'mapMaybe' g ≡ 'mapMaybe' (f <=< g)@
+class Functor f => Filterable f where
+  -- | Like 'Maybe.mapMaybe'.
+  mapMaybe :: (a -> Maybe b) -> f a -> f b
+  mapMaybe f = catMaybes . fmap f
+  {-# INLINE mapMaybe #-}
+
+  -- | @'catMaybes' ≡ 'mapMaybe' 'id'@
+  catMaybes :: f (Maybe a) -> f a
+  catMaybes = mapMaybe id
+  {-# INLINE catMaybes #-}
+
+  -- | @'filter' f . 'filter' g ≡ filter ('liftA2' ('&&') g f)@
+  filter :: (a -> Bool) -> f a -> f a
+  filter f = mapMaybe $ \a -> if f a then Just a else Nothing
+  {-# INLINE filter #-}
+
+  {-# MINIMAL mapMaybe | catMaybes #-}
+
+-- | An enhancement of 'Traversable' with 'Filterable'
+--
+-- A definition of 'wither' must satisfy the following laws:
+--
+-- [/conservation/]
+--   @'wither' ('fmap' 'Just' . f) ≡ 'traverse' f@
+--
+-- [/composition/]
+--   @'Compose' . 'fmap' ('wither' f) . 'wither' g ≡ 'wither' ('Compose' . 'fmap' ('wither' f) . g)@
+--
+-- Parametricity implies the naturality law:
+--
+-- Whenever @t@ is an //applicative transformation// in the sense described in the
+-- 'Traversable' documentation,
+--
+--   @t . 'wither' f ≡ 'wither' (t . f)@
+--
+-- See the @Properties.md@ file in the git distribution for some special properties of
+-- empty containers.
+
+class (T.Traversable t, Filterable t) => Witherable t where
+
+  -- | Effectful 'mapMaybe'.
+  --
+  -- @'wither' ('pure' . f) ≡ 'pure' . 'mapMaybe' f@
+  wither :: Applicative f => (a -> f (Maybe b)) -> t a -> f (t b)
+  wither f = fmap catMaybes . T.traverse f
+  {-# INLINE wither #-}
+
+  -- | @Monadic variant of 'wither'. This may have more efficient implementation.@
+  witherM :: Monad m => (a -> m (Maybe b)) -> t a -> m (t b)
+  witherM = wither
+
+  filterA :: Applicative f => (a -> f Bool) -> t a -> f (t a)
+  filterA f = wither $ \a -> (\b -> if b then Just a else Nothing) <$> f a
+
+  witherMap :: (Applicative m) => (t b -> r) -> (a -> m (Maybe b)) -> t a -> m r
+  witherMap p f = fmap p . wither f
+  {-# INLINE witherMap #-}
+
+  {-# MINIMAL #-}
+
+instance Filterable Maybe where
+  mapMaybe f = (>>= f)
+  {-# INLINE mapMaybe #-}
+
+instance Witherable Maybe where
+  wither _ Nothing = pure Nothing
+  wither f (Just a) = f a
+  {-# INLINABLE wither #-}
+
+instance Filterable Option where
+  mapMaybe f = (>>= Option . f)
+  {-# INLINE mapMaybe #-}
+
+instance Witherable Option where
+  wither f (Option x) = Option <$> wither f x
+  {-# INLINE wither #-}
+
+-- Option doesn't have the necessary instances in Lens
+--instance FilterableWithIndex () Option
+--instance WitherableWithIndex () Option
+
+instance Monoid e => Filterable (Either e) where
+  mapMaybe _ (Left e) = Left e
+  mapMaybe f (Right a) = maybe (Left mempty) Right $ f a
+  {-# INLINABLE mapMaybe #-}
+
+instance Monoid e => Witherable (Either e) where
+  wither _ (Left e) = pure (Left e)
+  wither f (Right a) = fmap (maybe (Left mempty) Right) (f a)
+  {-# INLINABLE wither #-}
+
+instance Filterable [] where
+  mapMaybe = Maybe.mapMaybe
+  catMaybes = Maybe.catMaybes
+  filter = Prelude.filter
+
+instance Filterable ZipList where
+  mapMaybe f = ZipList . Maybe.mapMaybe f . getZipList
+  catMaybes = ZipList . Maybe.catMaybes . getZipList
+  filter f = ZipList . Prelude.filter f . getZipList
+
+-- | Methods are good consumers for fusion.
+instance Witherable [] where
+  wither f = foldr go (pure []) where
+    go x r = liftA2 (maybe id (:)) (f x) r
+  {-# INLINE wither #-}
+  witherM f = foldr go (pure []) where
+    go x r = f x >>=
+      (\z -> case z of
+        Nothing -> r
+        Just y -> ((:) y) <$> r
+      )
+  {-# INLINE witherM #-}
+
+  -- Compared to the default, this fuses an fmap into a liftA2.
+  filterA p = go where
+    go (x:xs) = liftA2 (bool id (x :)) (p x) (go xs)
+    go [] = pure []
+
+instance Witherable ZipList where
+  wither f = fmap ZipList . wither f . getZipList
+
+instance Filterable IM.IntMap where
+  mapMaybe = IM.mapMaybe
+  filter = IM.filter
+
+instance Witherable IM.IntMap where
+
+instance Filterable (M.Map k) where
+  mapMaybe = M.mapMaybe
+  filter = M.filter
+
+instance Witherable (M.Map k) where
+#if MIN_VERSION_containers(0,5,8)
+  wither f = M.traverseMaybeWithKey (const f)
+#endif
+
+instance (Eq k, Hashable k) => Filterable (HM.HashMap k) where
+  mapMaybe = HM.mapMaybe
+  filter = HM.filter
+
+instance (Eq k, Hashable k) => Witherable (HM.HashMap k) where
+
+instance Filterable Proxy where
+ mapMaybe _ Proxy = Proxy
+
+instance Witherable Proxy where
+  wither _ Proxy = pure Proxy
+
+instance Filterable (Const r) where
+  mapMaybe _ (Const r) = Const r
+  {-# INLINABLE mapMaybe #-}
+
+instance Witherable (Const r) where
+  wither _ (Const r) = pure (Const r)
+  {-# INLINABLE wither #-}
+
+instance Filterable V.Vector where
+  mapMaybe = V.mapMaybe
+
+instance Witherable V.Vector where
+  wither f = fmap V.fromList . wither f . V.toList
+  {-# INLINABLE wither #-}
+
+instance Filterable S.Seq where
+  mapMaybe f = S.fromList . mapMaybe f . F.toList
+  {-# INLINABLE mapMaybe #-}
+  filter = S.filter
+
+instance Witherable S.Seq where
+  wither f = fmap S.fromList . wither f . F.toList
+  {-# INLINABLE wither #-}
+
+{-
+  -- TODO: try to figure out whether the following is better or worse for
+  -- typical applications. It builds the sequence incrementally rather than
+  -- building a list and converting.  This is basically the same approach
+  -- currently used by Data.Sequence.filter.
+
+  witherM f = F.foldlM go S.empty
+    where
+      --go :: S.Seq b -> a -> m (S.Seq b)
+      go s a = do
+        mb <- f a
+        case mb of
+          Nothing -> pure s
+          Just b -> pure $! s S.|> b
+  {-# INLINABLE witherM #-}
+-}
+
+-- The instances for Compose, Product, and Sum are not entirely
+-- unique. Any particular composition, product, or sum of functors
+-- may support a variety of 'wither' implementations.
+
+instance (Functor f, Filterable g) => Filterable (Compose f g) where
+  mapMaybe f = Compose . fmap (mapMaybe f) . getCompose
+  filter p = Compose . fmap (filter p) . getCompose
+  catMaybes = Compose . fmap catMaybes . getCompose
+
+instance (T.Traversable f, Witherable g) => Witherable (Compose f g) where
+  wither f = fmap Compose . T.traverse (wither f) . getCompose
+  witherM f = fmap Compose . T.mapM (witherM f) . getCompose
+  filterA p = fmap Compose . T.traverse (filterA p) . getCompose
+
+instance (Filterable f, Filterable g) => Filterable (P.Product f g) where
+  mapMaybe f (P.Pair x y) = P.Pair (mapMaybe f x) (mapMaybe f y)
+  filter p (P.Pair x y) = P.Pair (filter p x) (filter p y)
+  catMaybes (P.Pair x y) = P.Pair (catMaybes x) (catMaybes y)
+
+instance (Witherable f, Witherable g) => Witherable (P.Product f g) where
+  wither f (P.Pair x y) = liftA2 P.Pair (wither f x) (wither f y)
+  witherM f (P.Pair x y) = liftA2 P.Pair (witherM f x) (witherM f y)
+  filterA p (P.Pair x y) = liftA2 P.Pair (filterA p x) (filterA p y)
+
+instance (Filterable f, Filterable g) => Filterable (Sum.Sum f g) where
+  mapMaybe f (Sum.InL x) = Sum.InL (mapMaybe f x)
+  mapMaybe f (Sum.InR y) = Sum.InR (mapMaybe f y)
+
+  catMaybes (Sum.InL x) = Sum.InL (catMaybes x)
+  catMaybes (Sum.InR y) = Sum.InR (catMaybes y)
+
+  filter p (Sum.InL x) = Sum.InL (filter p x)
+  filter p (Sum.InR y) = Sum.InR (filter p y)
+
+instance (Witherable f, Witherable g) => Witherable (Sum.Sum f g) where
+  wither f (Sum.InL x) = Sum.InL <$> wither f x
+  wither f (Sum.InR y) = Sum.InR <$> wither f y
+
+  witherM f (Sum.InL x) = Sum.InL <$> witherM f x
+  witherM f (Sum.InR y) = Sum.InR <$> witherM f y
+
+  filterA f (Sum.InL x) = Sum.InL <$> filterA f x
+  filterA f (Sum.InR y) = Sum.InR <$> filterA f y
+
+deriving instance Filterable f => Filterable (IdentityT f)
+
+instance Witherable f => Witherable (IdentityT f) where
+  wither f (IdentityT m) = IdentityT <$> wither f m
+  witherM f (IdentityT m) = IdentityT <$> witherM f m
+  filterA p (IdentityT m) = IdentityT <$> filterA p m
+
+instance Functor f => Filterable (MaybeT f) where
+  mapMaybe f = MaybeT . fmap (mapMaybe f) . runMaybeT
+
+instance (T.Traversable t) => Witherable (MaybeT t) where
+  wither f = fmap MaybeT . T.traverse (wither f) . runMaybeT
+  witherM f = fmap MaybeT . T.mapM (wither f) . runMaybeT
+
+deriving instance Filterable t => Filterable (Reverse t)
+
+-- | Wither from right to left.
+instance Witherable t => Witherable (Reverse t) where
+  wither f (Reverse t) =
+    fmap Reverse . forwards $ wither (coerce f) t
+  -- We can't do anything special with witherM, because Backwards m is not
+  -- generally a Monad.
+  filterA f (Reverse t) =
+    fmap Reverse . forwards $ filterA (coerce f) t
+
+deriving instance Filterable t => Filterable (Backwards t)
+
+instance Witherable t => Witherable (Backwards t) where
+  wither f (Backwards xs) = Backwards <$> wither f xs
+  witherM f (Backwards xs) = Backwards <$> witherM f xs
+  filterA f (Backwards xs) = Backwards <$> filterA f xs
+
+instance Filterable Generics.V1 where
+  mapMaybe _ v = case v of {}
+  catMaybes v = case v of {}
+  filter _ v = case v of {}
+
+instance Witherable Generics.V1 where
+  wither _ v = pure $ case v of {}
+  filterA _ v = pure $ case v of {}
+
+instance Filterable Generics.U1 where
+  mapMaybe _ _ = Generics.U1
+  catMaybes _ = Generics.U1
+  filter _ _ = Generics.U1
+
+instance Witherable Generics.U1 where
+  wither _ _ = pure Generics.U1
+  filterA _ _ = pure Generics.U1
+
+instance Filterable (Generics.K1 i c) where
+  mapMaybe _ (Generics.K1 a) = Generics.K1 a
+  catMaybes (Generics.K1 a) = Generics.K1 a
+  filter _ (Generics.K1 a) = Generics.K1 a
+
+instance Witherable (Generics.K1 i c) where
+  wither _ (Generics.K1 a) = pure (Generics.K1 a)
+  filterA _ (Generics.K1 a) = pure (Generics.K1 a)
+
+instance Filterable f => Filterable (Generics.Rec1 f) where
+  mapMaybe f (Generics.Rec1 a) = Generics.Rec1 (mapMaybe f a)
+  catMaybes (Generics.Rec1 a) = Generics.Rec1 (catMaybes a)
+  filter f (Generics.Rec1 a) = Generics.Rec1 (filter f a)
+
+instance Witherable f => Witherable (Generics.Rec1 f) where
+  wither f (Generics.Rec1 a) = fmap Generics.Rec1 (wither f a)
+  witherM f (Generics.Rec1 a) = fmap Generics.Rec1 (witherM f a)
+  filterA f (Generics.Rec1 a) = fmap Generics.Rec1 (filterA f a)
+
+instance Filterable f => Filterable (Generics.M1 i c f) where
+  mapMaybe f (Generics.M1 a) = Generics.M1 (mapMaybe f a)
+  catMaybes (Generics.M1 a) = Generics.M1 (catMaybes a)
+  filter f (Generics.M1 a) = Generics.M1 (filter f a)
+
+instance Witherable f => Witherable (Generics.M1 i c f) where
+  wither f (Generics.M1 a) = fmap Generics.M1 (wither f a)
+  witherM f (Generics.M1 a) = fmap Generics.M1 (witherM f a)
+  filterA f (Generics.M1 a) = fmap Generics.M1 (filterA f a)
+
+instance (Filterable f, Filterable g) => Filterable ((Generics.:*:) f g) where
+  mapMaybe f (a Generics.:*: b) = mapMaybe f a Generics.:*: mapMaybe f b
+  catMaybes (a Generics.:*: b) = catMaybes a Generics.:*: catMaybes b
+  filter f (a Generics.:*: b) = filter f a Generics.:*: filter f b
+
+instance (Witherable f, Witherable g) => Witherable ((Generics.:*:) f g) where
+  wither f (a Generics.:*: b) = liftA2 (Generics.:*:) (wither f a) (wither f b)
+  witherM f (a Generics.:*: b) = liftA2 (Generics.:*:) (witherM f a) (witherM f b)
+  filterA f (a Generics.:*: b) = liftA2 (Generics.:*:) (filterA f a) (filterA f b)
+
+instance (Filterable f, Filterable g) => Filterable ((Generics.:+:) f g) where
+  mapMaybe f (Generics.L1 a) = Generics.L1 (mapMaybe f a)
+  mapMaybe f (Generics.R1 a) = Generics.R1 (mapMaybe f a)
+  catMaybes (Generics.L1 a) = Generics.L1 (catMaybes a)
+  catMaybes (Generics.R1 a) = Generics.R1 (catMaybes a)
+  filter f (Generics.L1 a) = Generics.L1 (filter f a)
+  filter f (Generics.R1 a) = Generics.R1 (filter f a)
+
+instance (Witherable f, Witherable g) => Witherable ((Generics.:+:) f g) where
+  wither f (Generics.L1 a) = fmap Generics.L1 (wither f a)
+  wither f (Generics.R1 a) = fmap Generics.R1 (wither f a)
+  witherM f (Generics.L1 a) = fmap Generics.L1 (witherM f a)
+  witherM f (Generics.R1 a) = fmap Generics.R1 (witherM f a)
+  filterA f (Generics.L1 a) = fmap Generics.L1 (filterA f a)
+  filterA f (Generics.R1 a) = fmap Generics.R1 (filterA f a)
+
+instance (Functor f, Filterable g) => Filterable ((Generics.:.:) f g) where
+  mapMaybe f = Generics.Comp1 . fmap (mapMaybe f) . Generics.unComp1
+  catMaybes = Generics.Comp1 . fmap catMaybes . Generics.unComp1
+  filter f = Generics.Comp1 . fmap (filter f) . Generics.unComp1
+
+instance (T.Traversable f, Witherable g) => Witherable ((Generics.:.:) f g) where
+  wither f = fmap Generics.Comp1 . T.traverse (wither f) . Generics.unComp1
+  witherM f = fmap Generics.Comp1 . T.mapM (witherM f) . Generics.unComp1
+  filterA f = fmap Generics.Comp1 . T.traverse (filterA f) . Generics.unComp1
+
+-- | Indexed variant of 'Filterable'.
+class (FunctorWithIndex i t, Filterable t) => FilterableWithIndex i t | t -> i where
+  imapMaybe :: (i -> a -> Maybe b) -> t a -> t b
+  imapMaybe f = catMaybes . imap f
+  {-# INLINE imapMaybe #-}
+
+  -- | @'ifilter' f . 'ifilter' g ≡ ifilter (\i -> 'liftA2' ('&&') (f i) (g i))@
+  ifilter :: (i -> a -> Bool) -> t a -> t a
+  ifilter f = imapMaybe $ \i a -> if f i a then Just a else Nothing
+  {-# INLINE ifilter #-}
+
+-- | Indexed variant of 'Witherable'.
+class (TraversableWithIndex i t, Witherable t) => WitherableWithIndex i t | t -> i where
+  -- | Effectful 'imapMaybe'.
+  --
+  -- @'iwither' (\ i -> 'pure' . f i) ≡ 'pure' . 'imapMaybe' f@
+  iwither :: (Applicative f) => (i -> a -> f (Maybe b)) -> t a -> f (t b)
+  iwither f = fmap catMaybes . itraverse f
+
+  -- | @Monadic variant of 'wither'. This may have more efficient implementation.@
+  iwitherM :: (Monad m) => (i -> a -> m (Maybe b)) -> t a -> m (t b)
+  iwitherM = iwither
+
+  ifilterA :: (Applicative f) => (i -> a -> f Bool) -> t a -> f (t a)
+  ifilterA f = iwither (\i a -> (\b -> if b then Just a else Nothing) <$> f i a)
+
+instance FilterableWithIndex () Maybe
+
+instance WitherableWithIndex () Maybe
+
+-- Option doesn't have the necessary instances in Lens
+--instance FilterableWithIndex () Option
+--instance WitherableWithIndex () Option
+
+instance FilterableWithIndex Int []
+
+instance FilterableWithIndex Int ZipList
+
+instance WitherableWithIndex Int []
+
+instance WitherableWithIndex Int ZipList
+
+instance FilterableWithIndex Int IM.IntMap where
+  imapMaybe = IM.mapMaybeWithKey
+  ifilter = IM.filterWithKey
+
+instance WitherableWithIndex Int IM.IntMap where
+
+instance FilterableWithIndex k (M.Map k) where
+  imapMaybe = M.mapMaybeWithKey
+  ifilter = M.filterWithKey
+
+instance WitherableWithIndex k (M.Map k) where
+#if MIN_VERSION_containers(0,5,8)
+  iwither = M.traverseMaybeWithKey
+#endif
+
+instance (Eq k, Hashable k) => FilterableWithIndex k (HM.HashMap k) where
+  imapMaybe = HM.mapMaybeWithKey
+  ifilter = HM.filterWithKey
+
+instance (Eq k, Hashable k) => WitherableWithIndex k (HM.HashMap k) where
+
+instance FilterableWithIndex Void Proxy
+
+instance WitherableWithIndex Void Proxy
+
+instance FilterableWithIndex Int V.Vector where
+  imapMaybe = V.imapMaybe
+  ifilter = V.ifilter
+
+instance WitherableWithIndex Int V.Vector
+
+instance FilterableWithIndex Int S.Seq
+
+instance WitherableWithIndex Int S.Seq
+
+instance (FunctorWithIndex i f, FilterableWithIndex j g) => FilterableWithIndex (i, j) (Compose f g) where
+  imapMaybe f = Compose . imap (\i -> imapMaybe (\j -> f (i, j))) . getCompose
+  ifilter p = Compose . imap (\i -> ifilter (\j -> p (i, j))) . getCompose
+
+instance (TraversableWithIndex i f, WitherableWithIndex j g) => WitherableWithIndex (i, j) (Compose f g) where
+  iwither f = fmap Compose . itraverse (\i -> iwither (\j -> f (i, j))) . getCompose
+  iwitherM f = fmap Compose . imapM (\i -> iwitherM (\j -> f (i, j))) . getCompose
+  ifilterA p = fmap Compose . itraverse (\i -> ifilterA (\j -> p (i, j))) . getCompose
+
+instance (FilterableWithIndex i f, FilterableWithIndex j g) => FilterableWithIndex (Either i j) (P.Product f g) where
+  imapMaybe f (P.Pair x y) = P.Pair (imapMaybe (f . Left) x) (imapMaybe (f . Right) y)
+  ifilter p (P.Pair x y) = P.Pair (ifilter (p . Left) x) (ifilter (p . Right) y)
+
+instance (WitherableWithIndex i f, WitherableWithIndex j g) => WitherableWithIndex (Either i j) (P.Product f g) where
+  iwither f (P.Pair x y) = liftA2 P.Pair (iwither (f . Left) x) (iwither (f . Right) y)
+  iwitherM f (P.Pair x y) = liftA2 P.Pair (iwitherM (f . Left) x) (iwitherM (f . Right) y)
+  ifilterA p (P.Pair x y) = liftA2 P.Pair (ifilterA (p . Left) x) (ifilterA (p . Right) y)
+
+instance (FilterableWithIndex i f, FilterableWithIndex j g) => FilterableWithIndex (Either i j) (Sum.Sum f g) where
+  imapMaybe f (Sum.InL x) = Sum.InL (imapMaybe (f . Left) x)
+  imapMaybe f (Sum.InR y) = Sum.InR (imapMaybe (f . Right) y)
+
+  ifilter f (Sum.InL x) = Sum.InL (ifilter (f . Left) x)
+  ifilter f (Sum.InR y) = Sum.InR (ifilter (f . Right) y)
+
+instance (WitherableWithIndex i f, WitherableWithIndex j g) => WitherableWithIndex (Either i j) (Sum.Sum f g) where
+  iwither f (Sum.InL x) = Sum.InL <$> iwither (f . Left) x
+  iwither f (Sum.InR y) = Sum.InR <$> iwither (f . Right) y
+
+  iwitherM f (Sum.InL x) = Sum.InL <$> iwitherM (f . Left) x
+  iwitherM f (Sum.InR y) = Sum.InR <$> iwitherM (f . Right) y
+
+  ifilterA f (Sum.InL x) = Sum.InL <$> ifilterA (f . Left) x
+  ifilterA f (Sum.InR y) = Sum.InR <$> ifilterA (f . Right) y
+
+deriving instance (FilterableWithIndex i f) => FilterableWithIndex i (IdentityT f)
+
+instance (WitherableWithIndex i f) => WitherableWithIndex i (IdentityT f) where
+  iwither f (IdentityT m) = IdentityT <$> iwither f m
+  iwitherM f (IdentityT m) = IdentityT <$> iwitherM f m
+  ifilterA p (IdentityT m) = IdentityT <$> ifilterA p m
+
+deriving instance FilterableWithIndex i t => FilterableWithIndex i (Reverse t)
+
+-- | Wither from right to left.
+instance WitherableWithIndex i t => WitherableWithIndex i (Reverse t) where
+  iwither f (Reverse t) = fmap Reverse . forwards $ iwither (\i -> Backwards . f i) t
+  -- We can't do anything special with iwitherM, because Backwards m is not
+  -- generally a Monad.
+  ifilterA p (Reverse t) = fmap Reverse . forwards $ ifilterA (\i -> Backwards . p i) t
+
+deriving instance FilterableWithIndex i t => FilterableWithIndex i (Backwards t)
+
+instance WitherableWithIndex i t => WitherableWithIndex i (Backwards t) where
+  iwither f (Backwards xs) = Backwards <$> iwither f xs
+  iwitherM f (Backwards xs) = Backwards <$> iwitherM f xs
+  ifilterA f (Backwards xs) = Backwards <$> ifilterA f xs
+
+-- | An infix alias for 'mapMaybe'. The name of the operator alludes
+-- to '<$>', and has the same fixity.
+--
+-- @since 0.3.1
+(<$?>) :: Filterable f => (a -> Maybe b) -> f a -> f b
+(<$?>) = mapMaybe
+infixl 4 <$?>
+
+-- | Flipped version of '<$?>', the 'Filterable' version of
+-- 'Data.Functor.<&>'. It has the same fixity as 'Data.Functor.<&>'.
+--
+-- @
+-- ('<&?>') = 'flip' 'mapMaybe'
+-- @
+--
+-- @since 0.3.1
+(<&?>) :: Filterable f => f a -> (a -> Maybe b) -> f b
+as <&?> f = mapMaybe f as
+infixl 1 <&?>
+
+-- | @'forMaybe' = 'flip' 'wither'@
+forMaybe :: (Witherable t, Applicative f) => t a -> (a -> f (Maybe b)) -> f (t b)
+forMaybe = flip wither
+{-# INLINE forMaybe #-}
+
+-- | Removes duplicate elements from a list, keeping only the first
+--   occurrence. This is asymptotically faster than using
+--   'Data.List.nub' from "Data.List".
+ordNub :: (Witherable t, Ord a) => t a -> t a
+ordNub t = evalState (witherM f t) Set.empty where
+    f a = state $ \s -> if Set.member a s
+      then (Nothing, s)
+      else (Just a, Set.insert a s)
+{-# INLINE ordNub #-}
+
+-- | Removes duplicate elements from a list, keeping only the first
+--   occurrence. This is usually faster than 'ordNub', especially for
+--   things that have a slow comparison (like 'String').
+hashNub :: (Witherable t, Eq a, Hashable a) => t a -> t a
+hashNub t = evalState (witherM f t) HSet.empty
+  where
+    f a = state $ \s -> if HSet.member a s
+      then (Nothing, s)
+      else (Just a, HSet.insert a s)
+{-# INLINE hashNub #-}
+
+-- | A default implementation for 'mapMaybe'.
+mapMaybeDefault :: (F.Foldable f, Alternative f) => (a -> Maybe b) -> f a -> f b
+mapMaybeDefault p = F.foldr (\x xs -> case p x of
+    Just a -> pure a <|> xs
+    _ -> xs) empty
+{-# INLINABLE mapMaybeDefault #-}
+
+-- | A default implementation for 'imapMaybe'.
+imapMaybeDefault :: (FoldableWithIndex i f, Alternative f) => (i -> a -> Maybe b) -> f a -> f b
+imapMaybeDefault p = ifoldr (\i x xs -> case p i x of
+    Just a -> pure a <|> xs
+    _ -> xs) empty
+{-# INLINABLE imapMaybeDefault #-}
+
+newtype WrappedFoldable f a = WrapFilterable {unwrapFoldable :: f a}
+  deriving (Functor, F.Foldable, T.Traversable, Applicative, Alternative)
+
+instance (FunctorWithIndex i f) => FunctorWithIndex i (WrappedFoldable f) where
+  imap f = WrapFilterable . imap f . unwrapFoldable
+
+instance (FoldableWithIndex i f) => FoldableWithIndex i (WrappedFoldable f) where
+  ifoldMap f = ifoldMap f . unwrapFoldable
+
+instance (TraversableWithIndex i f) => TraversableWithIndex i (WrappedFoldable f) where
+  itraverse f = fmap WrapFilterable . itraverse f . unwrapFoldable
+
+instance (F.Foldable f, Alternative f) => Filterable (WrappedFoldable f) where
+    {-#INLINE mapMaybe#-}
+    mapMaybe = mapMaybeDefault
+
+instance (FunctorWithIndex i f, FoldableWithIndex i f, Alternative f) => FilterableWithIndex i (WrappedFoldable f) where
+  {-# INLINE imapMaybe #-}
+  imapMaybe = imapMaybeDefault
+
+instance (Alternative f, T.Traversable f) => Witherable (WrappedFoldable f)
diff --git a/witherable.cabal b/witherable.cabal
--- a/witherable.cabal
+++ b/witherable.cabal
@@ -1,9 +1,10 @@
+cabal-version:       2.4
 name:                witherable
-version:             0.3.5
+version:             0.4
 synopsis:            filterable traversable
 description:         A stronger variant of `traverse` which can remove elements and generalised mapMaybe, catMaybes, filter
 homepage:            https://github.com/fumieval/witherable
-license:             BSD3
+license:             BSD-3-Clause
 license-file:        LICENSE
 author:              Fumiaki Kinoshita
 maintainer:          Fumiaki Kinoshita <fumiexcel@gmail.com>
@@ -11,7 +12,6 @@
 category:            Data
 build-type:          Simple
 extra-source-files:  CHANGELOG.md
-cabal-version:       >=1.10
 tested-With: GHC == 8.2.2, GHC == 8.4.4, GHC == 8.6.3, GHC == 8.8.1
 
 source-repository head
@@ -19,24 +19,25 @@
   location: https://github.com/fumieval/witherable.git
 
 library
-  exposed-modules:     Data.Witherable
+  exposed-modules:
+    Witherable
+    Data.Witherable
   -- other-modules:
   -- other-extensions:
   build-depends:       base == 4.*,
                        base-orphans,
                        containers >= 0.5,
                        hashable,
-                       lens,
-                       monoidal-containers,
                        transformers,
                        transformers-compat,
                        unordered-containers,
                        vector,
-                       witherable-class
+                       indexed-traversable,
+                       indexed-traversable-instances,
   if impl(ghc < 7.9)
     build-depends:     void
   hs-source-dirs:      src
-  ghc-options:         -Wall
+  ghc-options:         -Wall -Wcompat
   default-language:    Haskell2010
   if (impl(ghc>=8))
     ghc-options:       -Wcompat