diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,3 +1,7 @@
+# 1.0.3
+
+* sourceRandomWith [#19](https://github.com/fpco/conduit-combinators/pull/19)
+
 # 1.0.2
 
 * Make mapAccumWhile & mapAccumS strict in accumulator state [#18](https://github.com/fpco/conduit-combinators/pull/18)
diff --git a/Data/Conduit/Combinators.hs b/Data/Conduit/Combinators.hs
--- a/Data/Conduit/Combinators.hs
+++ b/Data/Conduit/Combinators.hs
@@ -47,6 +47,10 @@
     , sourceRandomN
     , sourceRandomGen
     , sourceRandomNGen
+    , sourceRandomWith
+    , sourceRandomNWith
+    , sourceRandomGenWith
+    , sourceRandomNGenWith
 
       -- ** Filesystem
     , sourceDirectory
@@ -452,7 +456,8 @@
 --
 -- Since 1.0.0
 sourceRandom :: (MWC.Variate a, MonadIO m) => Producer m a
-INLINE_RULE0(sourceRandom, initRepeat (liftIO MWC.createSystemRandom) (liftIO . MWC.uniform))
+sourceRandom = sourceRandomWith MWC.uniform
+{-# INLINE sourceRandom #-}
 
 -- | Create a stream of random values of length n, seeding from the system
 -- random number.
@@ -463,7 +468,8 @@
 sourceRandomN :: (MWC.Variate a, MonadIO m)
               => Int -- ^ count
               -> Producer m a
-INLINE_RULE(sourceRandomN, cnt, initReplicate (liftIO MWC.createSystemRandom) (liftIO . MWC.uniform) cnt)
+sourceRandomN cnt = sourceRandomNWith cnt MWC.uniform
+{-# INLINE sourceRandomN #-}
 
 -- | Create an infinite stream of random values, using the given random number
 -- generator.
@@ -474,7 +480,8 @@
 sourceRandomGen :: (MWC.Variate a, MonadBase base m, PrimMonad base)
                 => MWC.Gen (PrimState base)
                 -> Producer m a
-INLINE_RULE(sourceRandomGen, gen, initRepeat (return gen) (liftBase . MWC.uniform))
+sourceRandomGen gen = sourceRandomGenWith gen MWC.uniform
+{-# INLINE sourceRandomGen #-}
 
 -- | Create a stream of random values of length n, seeding from the system
 -- random number.
@@ -486,7 +493,54 @@
                  => MWC.Gen (PrimState base)
                  -> Int -- ^ count
                  -> Producer m a
-INLINE_RULE(sourceRandomNGen, gen cnt, initReplicate (return gen) (liftBase . MWC.uniform) cnt)
+sourceRandomNGen gen cnt = sourceRandomNGenWith gen cnt MWC.uniform
+{-# INLINE sourceRandomNGen #-}
+
+-- | Create an infinite stream of random values from an arbitrary distribution,
+-- seeding from the system random number.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomWith :: (MWC.Variate a, MonadIO m) => (MWC.GenIO -> SIO.IO a) -> Producer m a
+INLINE_RULE(sourceRandomWith, f, initRepeat (liftIO MWC.createSystemRandom) (liftIO . f))
+
+-- | Create a stream of random values of length n from an arbitrary
+-- distribution, seeding from the system random number.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomNWith :: (MWC.Variate a, MonadIO m)
+                  => Int -- ^ count
+                  -> (MWC.GenIO -> SIO.IO a)
+                  -> Producer m a
+INLINE_RULE(sourceRandomNWith, cnt f, initReplicate (liftIO MWC.createSystemRandom) (liftIO . f) cnt)
+
+-- | Create an infinite stream of random values from an arbitrary distribution,
+-- using the given random number generator.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomGenWith :: (MWC.Variate a, MonadBase base m, PrimMonad base)
+                    => MWC.Gen (PrimState base)
+                    -> (MWC.Gen (PrimState base) -> base a)
+                    -> Producer m a
+INLINE_RULE(sourceRandomGenWith, gen f, initRepeat (return gen) (liftBase . f))
+
+-- | Create a stream of random values of length n from an arbitrary
+-- distribution, seeding from the system random number.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomNGenWith :: (MWC.Variate a, MonadBase base m, PrimMonad base)
+                     => MWC.Gen (PrimState base)
+                     -> Int -- ^ count
+                     -> (MWC.Gen (PrimState base) -> base a)
+                     -> Producer m a
+INLINE_RULE(sourceRandomNGenWith, gen cnt f, initReplicate (return gen) (liftBase . f) cnt)
 
 -- | Stream the contents of the given directory, without traversing deeply.
 --
diff --git a/Data/Conduit/Combinators/Unqualified.hs b/Data/Conduit/Combinators/Unqualified.hs
--- a/Data/Conduit/Combinators/Unqualified.hs
+++ b/Data/Conduit/Combinators/Unqualified.hs
@@ -34,6 +34,10 @@
     , sourceRandomN
     , sourceRandomGen
     , sourceRandomNGen
+    , sourceRandomWith
+    , sourceRandomNWith
+    , sourceRandomGenWith
+    , sourceRandomNGenWith
 
       -- *** Filesystem
     , sourceDirectory
@@ -379,6 +383,56 @@
                  -> Producer m a
 sourceRandomNGen = CC.sourceRandomNGen
 {-# INLINE sourceRandomNGen #-}
+
+-- | Create an infinite stream of random values from an arbitrary distribution,
+-- seeding from the system random number.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomWith :: (MWC.Variate a, MonadIO m) => (MWC.GenIO -> SIO.IO a) -> Producer m a
+sourceRandomWith = CC.sourceRandomWith
+{-# INLINE sourceRandomWith #-}
+
+-- | Create a stream of random values of length n from an arbitrary
+-- distribution, seeding from the system random number.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomNWith :: (MWC.Variate a, MonadIO m)
+                  => Int -- ^ count
+                  -> (MWC.GenIO -> SIO.IO a)
+                  -> Producer m a
+sourceRandomNWith = CC.sourceRandomNWith
+{-# INLINE sourceRandomNWith #-}
+
+-- | Create an infinite stream of random values from an arbitrary distribution,
+-- using the given random number generator.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomGenWith :: (MWC.Variate a, MonadBase base m, PrimMonad base)
+                    => MWC.Gen (PrimState base)
+                    -> (MWC.Gen (PrimState base) -> base a)
+                    -> Producer m a
+sourceRandomGenWith = CC.sourceRandomGenWith
+{-# INLINE sourceRandomGenWith #-}
+
+-- | Create a stream of random values of length n from an arbitrary
+-- distribution, seeding from the system random number.
+--
+-- Subject to fusion
+--
+-- Since 1.0.3
+sourceRandomNGenWith :: (MWC.Variate a, MonadBase base m, PrimMonad base)
+                     => MWC.Gen (PrimState base)
+                     -> Int -- ^ count
+                     -> (MWC.Gen (PrimState base) -> base a)
+                     -> Producer m a
+sourceRandomNGenWith= CC.sourceRandomNGenWith
+{-# INLINE sourceRandomNGenWith #-}
 
 -- | Stream the contents of the given directory, without traversing deeply.
 --
diff --git a/conduit-combinators.cabal b/conduit-combinators.cabal
--- a/conduit-combinators.cabal
+++ b/conduit-combinators.cabal
@@ -1,5 +1,5 @@
 name:                conduit-combinators
-version:             1.0.2
+version:             1.0.3
 synopsis:            Commonly used conduit functions, for both chunked and unchunked data
 description:         Provides a replacement for Data.Conduit.List, as well as a convenient Conduit module.
 homepage:            https://github.com/fpco/conduit-combinators
@@ -25,7 +25,7 @@
                      , transformers
                      , transformers-base
                      , primitive
-                     , mono-traversable >= 0.4
+                     , mono-traversable >= 0.5
                      , vector
                      , text
                      , bytestring