diff --git a/Crypto/Number/Generate.hs b/Crypto/Number/Generate.hs
index 1f356e5..b27fae7 100644
--- a/Crypto/Number/Generate.hs
+++ b/Crypto/Number/Generate.hs
@@ -21,7 +21,7 @@ import           Crypto.Random.Types
 import           Control.Monad (when)
 import           Foreign.Ptr
 import           Foreign.Storable
-import           Data.Bits ((.|.), (.&.), shiftL, shiftR, complement)
+import           Data.Bits ((.|.), (.&.), shiftL, complement, testBit)
 import           Crypto.Internal.ByteArray (Bytes, ScrubbedBytes)
 import qualified Crypto.Internal.ByteArray as B
 
@@ -79,23 +79,48 @@ generateParams bits genTopPolicy generateOdd
     bit   = (bits - 1) `mod` 8;
     mask  = 0xff `shiftL` (bit + 1);
 
--- | generate a positive integer x, s.t. 0 <= x < m
-generateMax :: MonadRandom m => Integer -> m Integer
-generateMax 1 = return 0
-generateMax m
-    | m <= 0    = error "negative value for generateMax"
-    | otherwise = do
-        result <- randomInt bytesLength
-        let result' = result `shiftR` bitsPoppedOff
-        if result' >= m
-            then generateMax m
-            else return result'
+-- | Generate a positive integer x, s.t. 0 <= x < range
+generateMax :: MonadRandom m
+            => Integer  -- ^ range
+            -> m Integer
+generateMax range
+    | range <= 1      = return 0
+    | range < 127     = generateSimple
+    | canOverGenerate = loopGenerateOver tries
+    | otherwise       = loopGenerate tries
   where
-        bytesLength   = lengthBytes m
-        bitsLength    = log2 (m-1) + 1
-        bitsPoppedOff = 8 - (bitsLength `mod` 8)
+        -- this "generator" is mostly for quickcheck benefits. it'll be biased if
+        -- range is not a multiple of 2, but overall, no security should be
+        -- assumed for a number between 0 and 127.
+        generateSimple = flip mod range `fmap` generateParams bits Nothing False
 
-        randomInt nbBytes = os2ipBytes <$> getRandomBytes nbBytes
+        loopGenerate count
+            | count == 0 = error "internal: generateMax (normal) doesn't seems to work properly"
+            | otherwise  = do
+                r <- generateParams bits Nothing False
+                if isValid r then return r else loopGenerate (count-1)
+
+        loopGenerateOver count
+            | count == 0 = error "internal: generateMax (over) doesn't seems to work properly"
+            | otherwise  = do
+                r <- generateParams (bits+1) Nothing False
+                let r2 = r - range
+                    r3 = r2 - range
+                if isValid r
+                    then return r
+                    else if isValid r2
+                        then return r2
+                        else if isValid r3
+                            then return r3
+                            else loopGenerateOver (count-1)
+
+        bits            = numBits range
+        canOverGenerate = bits > 3 && not (range `testBit` (bits-2)) && not (range `testBit` (bits-3))
+
+        isValid n = n < range
+
+        tries :: Int
+        tries = 100
 
 -- | generate a number between the inclusive bound [low,high].
 generateBetween :: MonadRandom m => Integer -> Integer -> m Integer