diff --git a/Crypto/Number/Generate.hs b/Crypto/Number/Generate.hs
index 7d2bd12..d3fd23c 100644
--- a/Crypto/Number/Generate.hs
+++ b/Crypto/Number/Generate.hs
@@ -10,7 +10,6 @@ module Crypto.Number.Generate
     , generateParams
     , generateMax
     , generateBetween
-    , generateOfSize
     ) where
 
 import           Crypto.Internal.Imports
@@ -123,8 +122,6 @@ generateMax range
 
 -- | generate a number between the inclusive bound [low,high].
 generateBetween :: MonadRandom m => Integer -> Integer -> m Integer
-generateBetween low high = (low +) <$> generateMax (high - low + 1)
-
--- | generate a positive integer of a specific bit size.
-generateOfSize :: MonadRandom m => Int -> m Integer
-generateOfSize bits = generateParams bits (Just SetTwoHighest) False
+generateBetween low high
+    | low == 1  = generateMax high >>= \r -> if r == 0 then generateBetween low high else return r
+    | otherwise = (low +) <$> generateMax (high - low + 1)
diff --git a/Crypto/Number/Prime.hs b/Crypto/Number/Prime.hs
index e405de8..89a92da 100644
--- a/Crypto/Number/Prime.hs
+++ b/Crypto/Number/Prime.hs
@@ -53,7 +53,7 @@ generatePrime bits = do
 -- as such it shouldn't be used if this number is supposed to be kept safe.
 generateSafePrime :: MonadRandom m => Int -> m Integer
 generateSafePrime bits = do
-    sp <- generateOfSize bits
+    sp <- generateParams bits (Just SetTwoHighest) True
     let p = findPrimeFromWith (\i -> isProbablyPrime (2*i+1)) (sp `div` 2)
     return (2*p+1)