diff --git a/Data/Universe/Helpers.hs b/Data/Universe/Helpers.hs
--- a/Data/Universe/Helpers.hs
+++ b/Data/Universe/Helpers.hs
@@ -28,12 +28,20 @@
 -- output list. Elements from lists at lower index occur more frequently, but
 -- not exponentially so.
 diagonal :: [[a]] -> [a]
-diagonal xss = go ([], xss) where
+diagonal = concat . diagonals
+
+-- | Like 'diagonal', but expose a tiny bit more (non-semantic) information:
+-- if you lay out the input list in two dimensions, each list in the result
+-- will be one of the diagonals of the input. In particular, each element of
+-- the output will be a list whose elements are each from a distinct input
+-- list.
+diagonals :: [[a]] -> [[a]]
+diagonals = go [] where
 	-- it is critical for some applications that we start producing answers
 	-- before inspecting es_
-	go (b, es_) = [h | h:_ <- b] ++ case es_ of
-		[]   -> interleave ts
-		e:es -> go (e:ts, es)
+	go b es_ = [h | h:_ <- b] : case es_ of
+		[]   -> transpose ts
+		e:es -> go (e:ts) es
 		where ts = [t | _:t <- b]
 
 -- | Fair 2-way interleaving.
diff --git a/universe-base.cabal b/universe-base.cabal
--- a/universe-base.cabal
+++ b/universe-base.cabal
@@ -1,5 +1,5 @@
 name:                universe-base
-version:             1.0.1
+version:             1.0.2
 synopsis:            A class for finite and recursively enumerable types and some helper functions for enumerating them
 homepage:            https://github.com/dmwit/universe
 license:             BSD3
@@ -16,7 +16,7 @@
 source-repository this
     type:            git
     location:        https://github.com/dmwit/universe
-    tag:             base-1.0.1
+    tag:             base-1.0.2
 
 library
   exposed-modules:     Data.Universe.Class, Data.Universe.Helpers