diff --git a/Data/Semigroup/Foldable.hs b/Data/Semigroup/Foldable.hs
--- a/Data/Semigroup/Foldable.hs
+++ b/Data/Semigroup/Foldable.hs
@@ -17,11 +17,16 @@
   , foldMapDefault1
   ) where
 
-import Prelude hiding (foldr)
+import Control.Monad.Trans.Identity
 import Data.Foldable
+import Data.Functor.Identity
 import Data.Functor.Apply
-import Data.Semigroup
-import Data.Monoid
+import Data.Functor.Product
+import Data.Functor.Compose
+import Data.Semigroup hiding (Product)
+import Data.Monoid hiding (Product)
+import Data.Traversable.Instances ()
+import Prelude hiding (foldr)
 
 class Foldable t => Foldable1 t where
   fold1 :: Semigroup m => t m -> m
@@ -29,6 +34,18 @@
 
   foldMap1 f = maybe (error "foldMap1") id . getOption . foldMap (Option . Just . f) 
   fold1 = foldMap1 id
+
+instance Foldable1 Identity where
+  foldMap1 f = f . runIdentity
+
+instance Foldable1 m => Foldable1 (IdentityT m) where
+  foldMap1 f = foldMap1 f . runIdentityT
+
+instance (Foldable1 f, Foldable1 g) => Foldable1 (Compose f g) where
+  foldMap1 f = foldMap1 (foldMap1 f) . getCompose
+
+instance (Foldable1 f, Foldable1 g) => Foldable1 (Product f g) where
+  foldMap1 f (Pair a b) = foldMap1 f a <> foldMap1 f b
 
 newtype Act f a = Act { getAct :: f a }
 
diff --git a/Data/Semigroup/Traversable.hs b/Data/Semigroup/Traversable.hs
--- a/Data/Semigroup/Traversable.hs
+++ b/Data/Semigroup/Traversable.hs
@@ -15,10 +15,15 @@
   ) where
 
 import Control.Applicative
+import Control.Monad.Trans.Identity
+import Data.Functor.Identity
 import Data.Functor.Apply
+import Data.Functor.Product
+import Data.Functor.Compose
 import Data.Semigroup.Foldable
 import Data.Traversable
-import Data.Semigroup
+import Data.Semigroup hiding (Product)
+import Data.Traversable.Instances ()
 
 class (Foldable1 t, Traversable t) => Traversable1 t where
   traverse1 :: Apply f => (a -> f b) -> t a -> f (t b)
@@ -29,3 +34,15 @@
 
 foldMap1Default :: (Traversable1 f, Semigroup m) => (a -> m) -> f a -> m
 foldMap1Default f = getConst . traverse1 (Const . f)
+
+instance Traversable1 Identity where
+  traverse1 f = fmap Identity . f . runIdentity
+
+instance Traversable1 f => Traversable1 (IdentityT f) where
+  traverse1 f = fmap IdentityT . traverse1 f . runIdentityT
+
+instance (Traversable1 f, Traversable1 g) => Traversable1 (Compose f g) where
+  traverse1 f = fmap Compose . traverse1 (traverse1 f) . getCompose
+
+instance (Traversable1 f, Traversable1 g) => Traversable1 (Product f g) where
+  traverse1 f (Pair a b) = Pair <$> traverse1 f a <.> traverse1 f b
diff --git a/Data/Traversable/Instances.hs b/Data/Traversable/Instances.hs
new file mode 100644
--- /dev/null
+++ b/Data/Traversable/Instances.hs
@@ -0,0 +1,13 @@
+-- | Placeholders for missing instances of Traversable, until base catches up and adds them
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+module Data.Traversable.Instances where
+
+import Control.Monad.Trans.Identity
+import Data.Foldable
+import Data.Traversable
+
+instance Foldable m => Foldable (IdentityT m) where
+  foldMap f = foldMap f . runIdentityT
+
+instance Traversable m => Traversable (IdentityT m) where
+  traverse f = fmap IdentityT . traverse f . runIdentityT
diff --git a/semigroupoids.cabal b/semigroupoids.cabal
--- a/semigroupoids.cabal
+++ b/semigroupoids.cabal
@@ -1,6 +1,6 @@
 name:          semigroupoids
 category:      Control, Comonads
-version:       1.1.0
+version:       1.1.1
 license:       BSD3
 cabal-version: >= 1.6
 license-file:  LICENSE
@@ -80,5 +80,6 @@
     Data.Semigroupoid
     Data.Semigroupoid.Dual
     Data.Semigroupoid.Static
+    Data.Traversable.Instances
 
   ghc-options: -Wall