diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,9 @@
+5.5.2 [2020.02.13]
+------------------
+* Add `Cochoice`, `Costrong`, `Closed`, `Traversing`, and `Mapping` instances
+  for `Cayley`.
+* Add `Mapping` and `Traversing` instances for `Tannen`.
+
 5.5.1 [2019.11.26]
 ------------------
 * Add `Choice`, `Cochoice`, `Closed`, `Strong`, and `Costrong` instances for
diff --git a/profunctors.cabal b/profunctors.cabal
--- a/profunctors.cabal
+++ b/profunctors.cabal
@@ -1,6 +1,6 @@
 name:          profunctors
 category:      Control, Categories
-version:       5.5.1
+version:       5.5.2
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
diff --git a/src/Data/Profunctor/Cayley.hs b/src/Data/Profunctor/Cayley.hs
--- a/src/Data/Profunctor/Cayley.hs
+++ b/src/Data/Profunctor/Cayley.hs
@@ -19,6 +19,7 @@
 import Control.Comonad
 import Data.Profunctor
 import Data.Profunctor.Monad
+import Data.Profunctor.Traversing
 import Data.Profunctor.Unsafe
 import Prelude hiding ((.), id)
 
@@ -49,9 +50,28 @@
   first'  = Cayley . fmap first' . runCayley
   second' = Cayley . fmap second' . runCayley
 
+instance (Functor f, Costrong p) => Costrong (Cayley f p) where
+  unfirst (Cayley fp) = Cayley (fmap unfirst fp)
+  unsecond (Cayley fp) = Cayley (fmap unsecond fp)
+
 instance (Functor f, Choice p) => Choice (Cayley f p) where
   left'   = Cayley . fmap left' . runCayley
   right'  = Cayley . fmap right' . runCayley
+
+instance (Functor f, Cochoice p) => Cochoice (Cayley f p) where
+  unleft (Cayley fp) = Cayley (fmap unleft fp)
+  {-# INLINE unleft #-}
+  unright (Cayley fp) = Cayley (fmap unright fp)
+  {-# INLINE unright #-}
+
+instance (Functor f, Closed p) => Closed (Cayley f p) where
+  closed = Cayley . fmap closed . runCayley
+
+instance (Functor f, Traversing p) => Traversing (Cayley f p) where
+  traverse' = Cayley . fmap traverse' . runCayley
+
+instance (Functor f, Mapping p) => Mapping (Cayley f p) where
+  map' = Cayley . fmap map' . runCayley
 
 instance (Applicative f, Category p) => Category (Cayley f p) where
   id = Cayley $ pure id
diff --git a/src/Data/Profunctor/Mapping.hs b/src/Data/Profunctor/Mapping.hs
--- a/src/Data/Profunctor/Mapping.hs
+++ b/src/Data/Profunctor/Mapping.hs
@@ -24,6 +24,7 @@
   ) where
 
 import Control.Arrow (Kleisli(..))
+import Data.Bifunctor.Tannen
 import Data.Distributive
 import Data.Functor.Compose
 import Data.Functor.Identity
@@ -89,6 +90,9 @@
 instance (Applicative m, Distributive m) => Mapping (Star m) where
   map' (Star f) = Star (collect f)
   roam f = Star #. genMap f .# runStar
+
+instance (Functor f, Mapping p) => Mapping (Tannen f p) where
+  map' = Tannen . fmap map' . runTannen
 
 wanderMapping :: Mapping p => (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
 wanderMapping f = roam ((runIdentity .) #. f .# (Identity .))
diff --git a/src/Data/Profunctor/Traversing.hs b/src/Data/Profunctor/Traversing.hs
--- a/src/Data/Profunctor/Traversing.hs
+++ b/src/Data/Profunctor/Traversing.hs
@@ -20,6 +20,7 @@
 
 import Control.Applicative
 import Control.Arrow (Kleisli(..))
+import Data.Bifunctor.Tannen
 import Data.Functor.Compose
 import Data.Functor.Identity
 import Data.Orphans ()
@@ -135,6 +136,9 @@
 instance Applicative m => Traversing (Star m) where
   traverse' (Star m) = Star (traverse m)
   wander f (Star amb) = Star (f amb)
+
+instance (Functor f, Traversing p) => Traversing (Tannen f p) where
+  traverse' = Tannen . fmap traverse' . runTannen
 
 newtype CofreeTraversing p a b = CofreeTraversing { runCofreeTraversing :: forall f. Traversable f => p (f a) (f b) }