diff --git a/Data/Map/Ordered.hs b/Data/Map/Ordered.hs
--- a/Data/Map/Ordered.hs
+++ b/Data/Map/Ordered.hs
@@ -23,9 +23,10 @@
 	, (<|), (|<), (>|), (|>)
 	, (<>|), (|<>), unionWithL, unionWithR
 	, Bias(Bias, unbiased), L, R
-	-- * Deletion
+	-- * Deletion/Update
 	, delete, filter, (\\)
 	, (|/\), (/\|), intersectionWith
+	, alter
 	-- * Query
 	, null, size, member, notMember, lookup
 	-- * Indexing
diff --git a/Data/Map/Ordered/Internal.hs b/Data/Map/Ordered/Internal.hs
--- a/Data/Map/Ordered/Internal.hs
+++ b/Data/Map/Ordered/Internal.hs
@@ -2,10 +2,10 @@
 {-# LANGUAGE DeriveDataTypeable #-}
 {-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE TupleSections #-}
 
 module Data.Map.Ordered.Internal where
 
-import Control.Applicative ((<|>))
 import Control.Monad (guard)
 import Data.Data
 import Data.Foldable (Foldable, foldl', foldMap)
@@ -248,3 +248,12 @@
 -- /O(n)/, where /n/ is the size of the 'OMap'.
 toMap :: OMap k v -> Map k v
 toMap (OMap tvs _) = fmap snd tvs
+
+-- | Alter the value at k, or absence of. Can be used to insert delete or update
+--   with the same semantics as 'Map's alter
+alter :: Ord k => (Maybe v -> Maybe v) -> k -> OMap k v -> OMap k v
+alter f k om@(OMap tvs kvs) =
+  case fst <$> M.lookup k tvs of
+    Just t -> OMap (M.alter (fmap (t,) . f . fmap snd) k tvs)
+                   (M.alter (fmap (k,) . f . fmap snd) t kvs)
+    Nothing -> maybe om ((om |>) . (k, )) $ f Nothing
diff --git a/ordered-containers.cabal b/ordered-containers.cabal
--- a/ordered-containers.cabal
+++ b/ordered-containers.cabal
@@ -1,5 +1,5 @@
 name:                ordered-containers
-version:             0.2.2
+version:             0.2.3
 synopsis:            Set- and Map-like types that remember the order elements were inserted
 license:             BSD3
 license-file:        LICENSE