diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,6 +1,17 @@
 Changelog
 =========
 
+Version 0.3.1.0
+---------------
+
+*June 13, 2019*
+
+<https://github.com/mstksg/nonempty-containers/releases/tag/v0.3.1.0>
+
+*   Add `absurdNEMap` to *Data.Map.NonEmpty*.  This is the only type that would
+    benefit from such a specialized function, whereas all other types would do
+    just as well with `absurd . fold1 :: Foldable1 f => f Void -> a`.
+
 Version 0.3.0.0
 ---------------
 
diff --git a/nonempty-containers.cabal b/nonempty-containers.cabal
--- a/nonempty-containers.cabal
+++ b/nonempty-containers.cabal
@@ -4,10 +4,10 @@
 --
 -- see: https://github.com/sol/hpack
 --
--- hash: 87d86a711cd539b74db2c65e4aad0b063f44dcafe10649bef05ae1b731f9ea36
+-- hash: ba935c3c5707ed9ae691a7496155c303f8b100b1fb53ed3ada7af6de3a68b61d
 
 name:           nonempty-containers
-version:        0.3.0.0
+version:        0.3.1.0
 synopsis:       Non-empty variants of containers data types, with full API
 description:    Efficient and optimized non-empty versions of types from /containers/.
                 Inspired by /non-empty-containers/ library, except attempting a more
diff --git a/src/Data/Map/NonEmpty.hs b/src/Data/Map/NonEmpty.hs
--- a/src/Data/Map/NonEmpty.hs
+++ b/src/Data/Map/NonEmpty.hs
@@ -122,6 +122,7 @@
   , lookupGT
   , lookupLE
   , lookupGE
+  , absurdNEMap
 
   -- ** Size
   , size
@@ -264,6 +265,7 @@
 import           Data.Set                   (Set)
 import           Data.Set.NonEmpty.Internal (NESet(..))
 import           Data.These
+import           Data.Void
 import           Prelude hiding             (lookup, foldr1, foldl1, foldr, foldl, filter, map, take, drop, splitAt)
 import qualified Data.Foldable              as F
 import qualified Data.List.NonEmpty         as NE
@@ -2336,6 +2338,17 @@
                             . M.maxViewWithKey
                             $ m
 {-# INLINE deleteFindMax #-}
+
+-- | Special property of non-empty maps: The type of non-empty maps over
+-- uninhabited keys is itself uninhabited.
+--
+-- This property also exists for /values/ inside a non-empty container
+-- (like for 'NESet', 'NESeq', and 'NEIntMap'); this can be witnessed using
+-- the function @'absurd' . 'fold1'@.
+--
+-- @since 0.3.1.0
+absurdNEMap :: NEMap Void a -> b
+absurdNEMap (NEMap k _ _) = absurd k
 
 -- ---------------------------
 -- Combining functions