diff --git a/aeson-better-errors.cabal b/aeson-better-errors.cabal
--- a/aeson-better-errors.cabal
+++ b/aeson-better-errors.cabal
@@ -1,5 +1,5 @@
 name:                aeson-better-errors
-version:             0.4.0.1
+version:             0.5.0.0
 synopsis:            Better error messages when decoding JSON values.
 license:             MIT
 license-file:        LICENSE
diff --git a/src/Data/Aeson/BetterErrors.hs b/src/Data/Aeson/BetterErrors.hs
--- a/src/Data/Aeson/BetterErrors.hs
+++ b/src/Data/Aeson/BetterErrors.hs
@@ -15,6 +15,8 @@
   ( -- * The Parser type
     Parse
   , Parse'
+  , mapError
+  , (.!)
 
   -- * Basic parsers
   , asText
@@ -28,6 +30,8 @@
   , asArray
 
   -- * Traversing JSON
+  , perhaps
+
   , key
   , keyOrDefault
   , keyMay
diff --git a/src/Data/Aeson/BetterErrors/Internal.hs b/src/Data/Aeson/BetterErrors/Internal.hs
--- a/src/Data/Aeson/BetterErrors/Internal.hs
+++ b/src/Data/Aeson/BetterErrors/Internal.hs
@@ -1,4 +1,5 @@
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE OverloadedStrings #-}
 {-# LANGUAGE TupleSections #-}
 
@@ -46,6 +47,21 @@
   deriving (Functor, Applicative, Monad,
             MonadReader ParseReader, MonadError (ParseError err))
 
+runParse :: Parse err a -> A.Value -> Either (ParseError err) a
+runParse (Parse p) v = runExcept (runReaderT p (ParseReader DList.empty v))
+
+-- | Transform the error of a parser according to the given function.
+mapError :: (err -> err') -> Parse err a -> Parse err' a
+mapError f p = do
+  v <- asks rdrValue
+  case runParse p v of
+    Right x -> pure x
+    Left err -> throwError (f <$> err)
+
+-- | An infix version of 'mapError'.
+(.!) :: Parse err a -> (err -> err') -> Parse err' a
+(.!) = flip mapError
+
 -- | The type of parsers which never produce custom validation errors.
 type Parse' = Parse Void
 
@@ -54,12 +70,10 @@
   Parse err a ->
   s ->
   Either (ParseError err) a
-runParser decode (Parse p) src =
+runParser decode p src =
   case decode src of
     Left err -> Left (InvalidJSON err)
-    Right value ->
-      let initialReader = ParseReader DList.empty value
-      in  runExcept (runReaderT p initialReader)
+    Right value -> runParse p value
 
 -- | Run a parser with a lazy 'BL.ByteString' containing JSON data. Note that
 -- the normal caveat applies: the JSON supplied must contain either an object
@@ -119,7 +133,7 @@
 data ParseError err
   = InvalidJSON String
   | BadSchema [PathPiece] (ErrorSpecifics err)
-  deriving (Show, Eq)
+  deriving (Show, Eq, Functor)
 
 -- | Detailed information in the case where a value could be parsed as JSON,
 -- but a value of the required type could not be constructed from it, for some
@@ -130,7 +144,7 @@
   | WrongType JSONType A.Value -- ^ Expected type, actual value
   | ExpectedIntegral Double
   | CustomError err
-  deriving (Show, Eq)
+  deriving (Show, Eq, Functor)
 
 -- | An enumeration of the different types that JSON values may take.
 data JSONType
@@ -259,6 +273,16 @@
 -- the case where something is not null.
 asNull :: Parse err ()
 asNull = as patNull TyNull
+
+-- | Given a parser, transform it into a parser which returns @Nothing@ when
+-- supplied with a JSON @null@, and otherwise, attempts to parse with the
+-- original parser; if this succeeds, the result becomes a @Just@ value.
+perhaps :: Parse err a -> Parse err (Maybe a)
+perhaps p = do
+  v <- asks rdrValue
+  case v of
+    A.Null -> return Nothing
+    _      -> Just <$> p
 
 -- | Take the value corresponding to a given key in the current object.
 key :: Text -> Parse err a -> Parse err a