diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,6 +1,16 @@
 Changelog
 =========
 
+Version 0.3.4.3
+----------
+
+*August 25, 2021*
+
+<https://github.com/mstksg/nonempty-containers/releases/tag/v0.3.4.3>
+
+*   Fix `intersperse` for singleton non-empty sequences. (@eddiemundo)
+*   Fix `deleteMax` for singleton containers.
+
 Version 0.3.4.2
 ----------
 
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: af05370c135085af4252c99e5575aa4ba9ebe2bf244c46bffaee55772a7ccb53
+-- hash: c6b3bfa5e2f51136fd5cd80ba3505719544753478e23f5114f6c718a42120786
 
 name:           nonempty-containers
-version:        0.3.4.2
+version:        0.3.4.3
 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/IntMap/NonEmpty.hs b/src/Data/IntMap/NonEmpty.hs
--- a/src/Data/IntMap/NonEmpty.hs
+++ b/src/Data/IntMap/NonEmpty.hs
@@ -1800,7 +1800,9 @@
 -- > deleteMax (fromList ((5,"a") :| [(3,"b"), (7,"c")])) == Data.IntMap.fromList [(3,"b"), (5,"a")]
 -- > deleteMax (singleton 5 "a") == Data.IntMap.empty
 deleteMax :: NEIntMap a -> IntMap a
-deleteMax (NEIntMap k v m) = insertMinMap k v . M.deleteMax $ m
+deleteMax (NEIntMap k v m) = case M.maxView m of
+    Nothing      -> M.empty
+    Just (_, m') -> insertMinMap k v m'
 {-# INLINE deleteMax #-}
 
 -- | /O(1)/ if delete, /O(log n)/ otherwise. Update the value at the
diff --git a/src/Data/IntSet/NonEmpty.hs b/src/Data/IntSet/NonEmpty.hs
--- a/src/Data/IntSet/NonEmpty.hs
+++ b/src/Data/IntSet/NonEmpty.hs
@@ -700,7 +700,9 @@
 -- > deleteMax (fromList (5 :| [3, 7])) == Data.IntSet.fromList [3, 5]
 -- > deleteMax (singleton 5) == Data.IntSet.empty
 deleteMax :: NEIntSet -> IntSet
-deleteMax (NEIntSet x s) = insertMinSet x . S.deleteMax $ s
+deleteMax (NEIntSet x s) = case S.maxView s of
+    Nothing      -> S.empty
+    Just (_, s') -> insertMinSet x s'
 {-# INLINE deleteMax #-}
 
 -- | /O(1)/. Delete and find the minimal element.  It is constant-time, so
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
@@ -2203,7 +2203,9 @@
 -- > deleteMax (fromList ((5,"a") :| [(3,"b"), (7,"c")])) == Data.Map.fromList [(3,"b"), (5,"a")]
 -- > deleteMax (singleton 5 "a") == Data.Map.empty
 deleteMax :: NEMap k a -> Map k a
-deleteMax (NEMap k v m) = insertMinMap k v . M.deleteMax $ m
+deleteMax (NEMap k v m) = case M.maxView m of
+    Nothing      -> M.empty
+    Just (_, m') -> insertMinMap k v m'
 {-# INLINE deleteMax #-}
 
 -- | /O(1)/ if delete, /O(log n)/ otherwise. Update the value at the
diff --git a/src/Data/Sequence/NonEmpty.hs b/src/Data/Sequence/NonEmpty.hs
--- a/src/Data/Sequence/NonEmpty.hs
+++ b/src/Data/Sequence/NonEmpty.hs
@@ -957,7 +957,9 @@
 -- intersperse a (fromList [x,y,z]) = fromList [x,a,y,a,z]
 -- @
 intersperse :: a -> NESeq a -> NESeq a
-intersperse z (x :<|| xs) = x :<|| (z Seq.<| Seq.intersperse z xs)
+intersperse z nes@(x :<|| xs) = case xs of
+  _ Seq.:<| _ -> x :<|| (z Seq.<| Seq.intersperse z xs)
+  Seq.Empty -> nes
 {-# INLINE intersperse #-}
 
 -- | \( O(\min(n_1,n_2,n_3)) \).  'zip3' takes three sequences and returns a
diff --git a/src/Data/Set/NonEmpty.hs b/src/Data/Set/NonEmpty.hs
--- a/src/Data/Set/NonEmpty.hs
+++ b/src/Data/Set/NonEmpty.hs
@@ -974,7 +974,9 @@
 -- > deleteMax (fromList (5 :| [3, 7])) == Data.Set.fromList [3, 5]
 -- > deleteMax (singleton 5) == Data.Set.empty
 deleteMax :: NESet a -> Set a
-deleteMax (NESet x s) = insertMinSet x . S.deleteMax $ s
+deleteMax (NESet x s) = case S.maxView s of
+    Nothing      -> S.empty
+    Just (_, s') -> insertMinSet x s'
 {-# INLINE deleteMax #-}
 
 -- | /O(1)/. Delete and find the minimal element.  It is constant-time, so
diff --git a/test/Tests/Util.hs b/test/Tests/Util.hs
--- a/test/Tests/Util.hs
+++ b/test/Tests/Util.hs
@@ -514,7 +514,7 @@
 valGen = Gen.text (Range.linear 0 5) Gen.alphaNum
 
 mapSize :: Range Int
-mapSize = Range.exponential 4 8
+mapSize = Range.exponential 1 8
 
 mapGen :: MonadGen m => m (Map KeyType Text)
 mapGen = Gen.map mapSize $ (,) <$> keyGen <*> valGen