diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,8 @@
+1.1.1
+-----
+* Backported a more efficient `Binary` instance for `Nat`
+* Allow `binary-0.8`
+
 1.1
 ---
 * Backported `Lift` instances.
diff --git a/nats.cabal b/nats.cabal
--- a/nats.cabal
+++ b/nats.cabal
@@ -1,6 +1,6 @@
 name:          nats
 category:      Numeric, Algebra
-version:       1.1
+version:       1.1.1
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
@@ -71,7 +71,7 @@
     build-depends: base >= 2 && < 5
 
     if flag(binary)
-      build-depends: binary >= 0.2 && < 0.8
+      build-depends: binary >= 0.2 && < 0.9
 
     if flag(template-haskell)
       build-depends: template-haskell >= 2.2 && < 2.12
diff --git a/src/Numeric/Natural.hs b/src/Numeric/Natural.hs
--- a/src/Numeric/Natural.hs
+++ b/src/Numeric/Natural.hs
@@ -39,7 +39,7 @@
 #ifdef MIN_VERSION_binary
 import Control.Monad (liftM)
 import Data.Binary (Binary(..), Get, Word8, Word64, putWord8)
-import Data.List (unfoldr)
+import Data.List (foldl', unfoldr)
 #endif
 
 import Data.Bits
@@ -234,16 +234,16 @@
 --
 -- Fold and unfold an Integer to and from a list of its bytes
 --
-unroll :: (Integral a, Num a, Bits a) => a -> [Word8]
+unroll :: (Integral a, Bits a) => a -> [Word8]
 unroll = unfoldr step
   where
     step 0 = Nothing
     step i = Just (fromIntegral i, i `shiftR` 8)
 
-roll :: (Integral a, Num a, Bits a) => [Word8] -> a
-roll   = foldr unstep 0
+roll :: (Integral a, Bits a) => [Word8] -> a
+roll   = foldl' unstep 0 . reverse
   where
-    unstep b a = a `shiftL` 8 .|. fromIntegral b
+    unstep a b = a `shiftL` 8 .|. fromIntegral b
 
 -- Fixed-size type for a subset of Natural
 type NaturalWord = Word64