diff --git a/CHANGES.markdown b/CHANGES.markdown
--- a/CHANGES.markdown
+++ b/CHANGES.markdown
@@ -1,3 +1,7 @@
+## Changes in 0.3.2
+ - `Storable (Complex a)` instance no longer requires a `RealFloat a`
+   constraint if using `base-4.4` or later
+
 ## Changes in 0.3.1
  - `Functor`, `Applicative`, and `Monad` instances for `First` and `Last`
 
diff --git a/base-orphans.cabal b/base-orphans.cabal
--- a/base-orphans.cabal
+++ b/base-orphans.cabal
@@ -3,7 +3,7 @@
 -- see: https://github.com/sol/hpack
 
 name:                base-orphans
-version:             0.3.1
+version:             0.3.2
 synopsis:            Backwards-compatible orphan instances for base
 homepage:            https://github.com/haskell-compat/base-orphans#readme
 bug-reports:         https://github.com/haskell-compat/base-orphans/issues
diff --git a/src/Data/Orphans.hs b/src/Data/Orphans.hs
--- a/src/Data/Orphans.hs
+++ b/src/Data/Orphans.hs
@@ -93,7 +93,7 @@
 #endif
 
 #if !(MIN_VERSION_base(4,8,0))
-import Data.Complex (Complex(..), realPart)
+import Data.Complex (Complex(..))
 import Data.Version
 import Foreign.Ptr (castPtr)
 import GHC.Real (Ratio(..), (%))
@@ -1161,12 +1161,16 @@
 deriving instance Applicative Last
 deriving instance Monad Last
 
--- The actual constraint in base-4.8.0.0 doesn't include RealFloat a, but it
--- is needed in previous versions of base due to Complex having lots of
--- RealFloat constraints in its functions' type signatures.
-instance (Storable a, RealFloat a) => Storable (Complex a) where
-    sizeOf a       = 2 * sizeOf (realPart a)
-    alignment a    = alignment (realPart a)
+-- In base-4.3 and earlier, pattern matching on a Complex value invokes a
+-- RealFloat constraint due to the use of the DatatypeContexts extension.
+# if MIN_VERSION_base(4,4,0)
+instance Storable a
+# else
+instance (Storable a, RealFloat a)
+# endif
+  => Storable (Complex a) where
+    sizeOf (a :+ _)    = 2 * sizeOf a
+    alignment (a :+ _) = alignment a
     peek p           = do
                         q <- return $ castPtr p
                         r <- peek q