diff --git a/src/Cryptol/Testing/Concrete.hs b/src/Cryptol/Testing/Concrete.hs
index 458e22d5..8c8af0e0 100644
--- a/src/Cryptol/Testing/Concrete.hs
+++ b/src/Cryptol/Testing/Concrete.hs
@@ -90,8 +90,8 @@ typeSize ty =
         (TCBit, _)       -> Just 2
         (TCInteger, _)   -> Nothing
         (TCIntMod, [sz]) -> case tNoUser sz of
-                              TCon (TC (TCNum n)) _ -> Just n
-                              _                     -> Nothing
+                              TCon (TC (TCNum n)) _ | 0 < n -> Just n
+                              _                             -> Nothing
         (TCIntMod, _)    -> Nothing
         (TCSeq, [sz,el]) -> case tNoUser sz of
                               TCon (TC (TCNum n)) _ -> (^ n) <$> typeSize el
diff --git a/src/Cryptol/Testing/Random.hs b/src/Cryptol/Testing/Random.hs
index 5a13b4a4..24986c1a 100644
--- a/src/Cryptol/Testing/Random.hs
+++ b/src/Cryptol/Testing/Random.hs
@@ -72,6 +72,12 @@ randomValue ty =
 
         (TC TCInteger, [])                    -> Just randomInteger
 
+        (TC TCIntMod, [TCon (TC TCInf) []])   -> Just randomInteger
+
+        (TC TCIntMod, [TCon (TC (TCNum n)) []])
+          | 0 < n     -> Just (randomIntMod n)
+          | otherwise -> Just randomInteger
+
         (TC TCSeq, [TCon (TC TCInf) [], el])  ->
           do mk <- randomValue el
              return (randomStream mk)
@@ -114,6 +120,11 @@ randomInteger _ g =
       (x, g2) = randomR (- 256^n, 256^n) g1
   in (VInteger (integerLit x), g2)
 
+randomIntMod :: (BitWord b w i, RandomGen g) => Integer -> Gen g b w i
+randomIntMod modulus _ g =
+  let (x, g') = randomR (0, modulus-1) g
+  in (VInteger (integerLit x), g')
+
 -- | Generate a random word of the given length (i.e., a value of type @[w]@)
 -- The size parameter is assumed to vary between 1 and 100, and we use
 -- it to generate smaller numbers first.