diff --git a/Crypto/Number/Generate.hs b/Crypto/Number/Generate.hs
--- a/Crypto/Number/Generate.hs
+++ b/Crypto/Number/Generate.hs
@@ -11,31 +11,20 @@
     , generateOfSize
     ) where
 
-import Crypto.Number.Basic
 import Crypto.Number.Serialize
 import Crypto.Random.API
 import qualified Data.ByteString as B
-import Data.Bits ((.|.), (.&.), shiftL)
+import Data.Bits ((.|.))
 
--- | generate a positive integer x, s.t. 0 <= x < m, uniformly at random
+-- | generate a positive integer x, s.t. 0 <= x < m
+--
+-- Note that depending on m value, the number distribution
+-- generated by this function is not necessarily uniform.
 generateMax :: CPRG g => g -> Integer -> (Integer, g)
-generateMax rng m
-    | m < 1 = error "generateMax: m must be >= 1"
-    | m == 1 = (0,rng)
-    | otherwise =
-        let (tentativeResult, rng') =
-                withRandomBytes rng (lengthBytes m) $ \bs ->
-                    let lengthBits = (log2 (m-1) + 1)
-                        mask = if lengthBits `mod` 8 == 0
-                               then 0xff
-                               else (1 `shiftL` (lengthBits `mod` 8)) - 1 in
-                    os2ip $ snd $ B.mapAccumL (\acc w -> (0xff, w .&. acc))
-                                      mask bs in
-        if tentativeResult < m
-            then (tentativeResult, rng')
-            else generateMax rng' m
+generateMax rng m = withRandomBytes rng (lengthBytes m) $ \bs ->
+    os2ip bs `mod` m
 
--- | generate a number between the inclusive bound [low,high] uniformly at random.
+-- | generate a number between the inclusive bound [low,high].
 generateBetween :: CPRG g => g -> Integer -> Integer -> (Integer, g)
 generateBetween rng low high = (low + v, rng')
     where (v, rng') = generateMax rng (high - low + 1)
diff --git a/crypto-numbers.cabal b/crypto-numbers.cabal
--- a/crypto-numbers.cabal
+++ b/crypto-numbers.cabal
@@ -1,5 +1,5 @@
 Name:                crypto-numbers
-Version:             0.2.4
+Version:             0.2.5
 Description:         Cryptographic numbers: functions and algorithms
 License:             BSD3
 License-file:        LICENSE