diff --git a/Data/Filtrable.hs b/Data/Filtrable.hs
--- a/Data/Filtrable.hs
+++ b/Data/Filtrable.hs
@@ -7,11 +7,13 @@
 import Prelude hiding (filter)
 
 import Control.Applicative
+import Control.Applicative.Backwards
 import Control.Monad
 import qualified Control.Monad.Trans.State as M
 import Data.Bool (bool)
 import Data.Functor.Compose
 import Data.Functor.Product
+import Data.Functor.Reverse
 import Data.Functor.Sum
 import Data.Proxy
 import Data.Traversable
@@ -92,12 +94,19 @@
     mapMaybe f (Pair as bs) = Pair (mapMaybe f as) (mapMaybe f bs)
 
 instance (Filtrable f, Filtrable g) => Filtrable (Sum f g) where
-    mapMaybe f (InL as) = InL (mapMaybe f as)
-    mapMaybe f (InR bs) = InR (mapMaybe f bs)
+    mapMaybe f = \ case
+        InL as -> InL (mapMaybe f as)
+        InR bs -> InR (mapMaybe f bs)
 
 instance (Functor f, Filtrable g) => Filtrable (Compose f g) where
-    mapMaybe f (Compose as) = Compose (mapMaybe f <$> as)
+    mapMaybe f = Compose . (fmap . mapMaybe) f . getCompose
 
+instance Filtrable f => Filtrable (Backwards f) where
+    mapMaybe f = Backwards . mapMaybe f . forwards
+
+instance Filtrable f => Filtrable (Reverse f) where
+    mapMaybe f = Reverse . mapMaybe f . getReverse
+
 infixl 4 <$?>, <*?>
 
 (<$?>) :: Filtrable f => (a -> Maybe b) -> f a -> f b
@@ -119,12 +128,12 @@
     let b = all (not . eq a) as
     b <$ when b (M.modify (a:))
 
--- | \(\mathcal{O}(n^2)\)
+-- | \(\mathcal{O}(n\;\mathrm{log}\;n)\)
 -- Delete all but the first copy of each element, special case of 'nubOrdBy'.
 nubOrd :: (Filtrable f, Traversable f, Ord a) => f a -> f a
 nubOrd = nubOrdBy compare
 
--- | \(\mathcal{O}(n^2)\)
+-- | \(\mathcal{O}(n\;\mathrm{log}\;n)\)
 -- Delete all but the first copy of each element, with the given relation.
 nubOrdBy :: (Filtrable f, Traversable f) => (a -> a -> Ordering) -> f a -> f a
 nubOrdBy compare = fmap (flip M.evalState Set.empty) . filterA $ \ a -> M.state $ \ as ->
diff --git a/filtrable.cabal b/filtrable.cabal
--- a/filtrable.cabal
+++ b/filtrable.cabal
@@ -1,5 +1,5 @@
 name:                filtrable
-version:             0.1.4.0
+version:             0.1.5.0
 synopsis:            Class of filtrable containers
 homepage:            https://github.com/strake/filtrable.hs
 license:             BSD3
@@ -34,3 +34,14 @@
                        -Werror=incomplete-record-updates
                        -Werror=missing-fields
                        -Werror=missing-methods
+
+test-suite test
+  type:                exitcode-stdio-1.0
+  hs-source-dirs:      test
+  main-is:             Spec.hs
+  default-language:    Haskell2010
+  build-depends:       base >=4.9 && <5
+                     , filtrable
+                     , smallcheck >=1.2 && <1.3
+                     , tasty >=1.3.1 && <1.4
+                     , tasty-smallcheck >=0.8.1 && <0.9
diff --git a/test/Spec.hs b/test/Spec.hs
new file mode 100644
--- /dev/null
+++ b/test/Spec.hs
@@ -0,0 +1,32 @@
+{-# LANGUAGE PartialTypeSignatures #-}
+
+module Main (main) where
+
+import Prelude hiding (filter)
+import Control.Applicative
+import Data.Foldable
+import Data.Filtrable
+import qualified Data.List as List
+import Test.SmallCheck
+import Test.Tasty
+import Test.Tasty.SmallCheck
+
+main :: IO ()
+main = defaultMain $ testGroup ""
+  [ testGroup "Filtrable"
+      [ testProperty "filter" (prop_filter :: _ -> [Maybe Bool] -> _)
+      ]
+  , testGroup "nub"
+      [ testProperty "nub" (prop_nub :: [Int] -> _)
+      , testProperty "nubOrd" (prop_nubOrd :: [Int] -> _)
+      ] 
+  ]
+
+prop_filter :: (Filtrable f, Foldable f) => (a -> Bool) -> f a -> Bool
+prop_filter = liftA2 (.) all filter
+
+prop_nub :: (Filtrable f, Traversable f, Eq a) => f a -> Bool
+prop_nub = (==) <$> List.nub . toList <*> toList . nub
+
+prop_nubOrd :: (Filtrable f, Traversable f, Ord a) => f a -> Bool
+prop_nubOrd = (==) <$> List.nub . toList <*> toList . nubOrd