diff --git a/Crypto/Random.hs b/Crypto/Random.hs
index 37d4124..4cea74b 100644
--- a/Crypto/Random.hs
+++ b/Crypto/Random.hs
@@ -80,6 +80,10 @@ drgNewSeed (Seed seed) = initialize seed
 --
 -- It can also be used in other contexts provided the input
 -- has been properly randomly generated.
+--
+-- Note that the @Arbitrary@ instance provided by QuickCheck for 'Word64' does
+-- not have a uniform distribution.  It is often better to use instead
+-- @arbitraryBoundedRandom@.
 drgNewTest :: (Word64, Word64, Word64, Word64, Word64) -> ChaChaDRG
 drgNewTest = initializeWords
 
diff --git a/tests/Utils.hs b/tests/Utils.hs
index 03ba521..bf16bb4 100644
--- a/tests/Utils.hs
+++ b/tests/Utils.hs
@@ -19,7 +19,7 @@ newtype TestDRG = TestDRG (Word64, Word64, Word64, Word64, Word64)
     deriving (Show,Eq)
 
 instance Arbitrary TestDRG where
-    arbitrary = TestDRG `fmap` arbitrary
+    arbitrary = TestDRG `fmap` arbitrary  -- distribution not uniform
 
 withTestDRG (TestDRG l) f = fst $ withDRG (drgNewTest l) f