diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -5,7 +5,7 @@
 ## Unreleased changes
 
 
-## 0.7.0.0
+## 0.7.0.1
 
 -   Use random-1.2. This means, that the random number generator type has changed
     from `GenIO` (`System.Random.MWC`) to `IOGenM StdGen`
diff --git a/bench/Bench.hs b/bench/Bench.hs
--- a/bench/Bench.hs
+++ b/bench/Bench.hs
@@ -30,7 +30,7 @@
 
 main :: IO ()
 main = do
-  g <- newIOGenM $ mkStdGen 0
+  let g = mkStdGen 0
   defaultMain
     [ bgroup
         "Normal"
diff --git a/bench/Normal.hs b/bench/Normal.hs
--- a/bench/Normal.hs
+++ b/bench/Normal.hs
@@ -42,7 +42,7 @@
 mon :: Monitor Double
 mon = Monitor monStd [] []
 
-normalSlideBench :: IOGenM StdGen -> IO ()
+normalSlideBench :: StdGen -> IO ()
 normalSlideBench g = do
   let s =
         Settings
@@ -64,7 +64,7 @@
     [slideSymmetric 1.0 (PName $ "Medium " ++ show i) (pWeight 1) Tune | i <- [0 .. 100 :: Int]]
 
 -- Should have the same run time as 'normalSlide'.
-normalLargeCycleBench :: IOGenM StdGen -> IO ()
+normalLargeCycleBench :: StdGen -> IO ()
 normalLargeCycleBench g = do
   let s =
         Settings
@@ -83,7 +83,7 @@
 ccBactrian :: Cycle Double
 ccBactrian = cycleFromList [slideBactrian 0.5 1.0 (PName "Bactrian") (pWeight 1) Tune]
 
-normalBactrianBench :: IOGenM StdGen -> IO ()
+normalBactrianBench :: StdGen -> IO ()
 normalBactrianBench g = do
   let s =
         Settings
@@ -99,7 +99,7 @@
   a <- mhg s noPrior lh ccBactrian mon 0 g
   void $ mcmc s a
 
-normalMC3 :: IOGenM StdGen -> Int -> IO ()
+normalMC3 :: StdGen -> Int -> IO ()
 normalMC3 g n = do
   let mcmcS =
         Settings
diff --git a/bench/Poisson.hs b/bench/Poisson.hs
--- a/bench/Poisson.hs
+++ b/bench/Poisson.hs
@@ -86,7 +86,7 @@
 mon :: Monitor I
 mon = Monitor monStd [] []
 
-poissonBench :: IOGenM StdGen -> IO ()
+poissonBench :: StdGen -> IO ()
 poissonBench g = do
   let s =
         Settings
@@ -123,7 +123,7 @@
 hmcProposal :: Cycle I
 hmcProposal = cycleFromList [hamiltonian hparams htconf hstruct target (PName "Hamiltonian") (pWeight 1)]
 
-poissonHamiltonianBench :: IOGenM StdGen -> IO ()
+poissonHamiltonianBench :: StdGen -> IO ()
 poissonHamiltonianBench g = do
   let s =
         Settings
diff --git a/mcmc.cabal b/mcmc.cabal
--- a/mcmc.cabal
+++ b/mcmc.cabal
@@ -1,6 +1,6 @@
 cabal-version:      3.0
 name:               mcmc
-version:            0.7.0.0
+version:            0.7.0.1
 synopsis:           Sample from a posterior using Markov chain Monte Carlo
 description:
   Please see the README on GitHub at <https://github.com/dschrempf/mcmc#readme>
diff --git a/src/Mcmc/Algorithm.hs b/src/Mcmc/Algorithm.hs
--- a/src/Mcmc/Algorithm.hs
+++ b/src/Mcmc/Algorithm.hs
@@ -30,7 +30,7 @@
 
   -- | Check if the current state is invalid. At the moment this should just
   -- check if the posterior probability is zero or NaN.
-  aIsInValidState :: a -> Bool
+  aIsInvalidState :: a -> Bool
 
   -- | Sample the next state.
   aIterate :: IterationMode -> ParallelizationMode -> a -> IO a
@@ -48,7 +48,7 @@
   -- the trace, if required.
   aCleanAfterBurnIn :: TraceLength -> a -> IO a
 
-  -- | Summarize the cycle.
+  -- | Summarize the proposals in the cycle.
   aSummarizeCycle :: IterationMode -> a -> BL.ByteString
 
   -- | Open required monitor files and setup corresponding file handles.
diff --git a/src/Mcmc/Algorithm/MC3.hs b/src/Mcmc/Algorithm/MC3.hs
--- a/src/Mcmc/Algorithm/MC3.hs
+++ b/src/Mcmc/Algorithm/MC3.hs
@@ -179,7 +179,7 @@
 instance ToJSON a => Algorithm (MC3 a) where
   aName = const "Metropolis-coupled Markov chain Monte Carlo (MC3)"
   aIteration = mc3Iteration
-  aIsInValidState = mc3IsInValidState
+  aIsInvalidState = mc3IsInvalidState
   aIterate = mc3Iterate
   aAutoTune = mc3AutoTune
   aResetAcceptance = mc3ResetAcceptance
@@ -265,10 +265,6 @@
     l = link c
     t = trace c
 
--- TODO (medium): Splitmix. Initialization of the MC3 algorithm is an IO action
--- because the generators have to be split. And also because of the mutable
--- trace.
-
 -- | Initialize an MC3 algorithm with a given number of chains.
 --
 -- Call 'error' if:
@@ -284,19 +280,21 @@
   Cycle a ->
   Monitor a ->
   InitialState a ->
-  IOGenM StdGen ->
+  StdGen ->
   IO (MC3 a)
 mc3 sMc3 s pr lh cc mn i0 g
   | n < 2 = error "mc3: The number of chains must be two or larger."
   | sp < 1 = error "mc3: The swap period must be strictly positive."
   | sn < 1 || sn > n - 1 = error "mc3: The number of swaps must be in [1, NChains - 1]."
   | otherwise = do
-      -- Split random number generators.
-      rs <- replicateM n $ splitGenM g
-      gs <- V.fromList <$> mapM newIOGenM rs
-      cs <- V.mapM (mhg s pr lh cc mn i0) gs
+      -- Split random number generator.
+      let gs = take (n + 1) $ unfoldr (Just . split) g
+      -- Prepare MHG chains.
+      cs <- V.mapM (mhg s pr lh cc mn i0) (V.fromList $ tail gs)
       hcs <- V.izipWithM (initMHG pr lh) (V.convert bs) cs
-      return $ MC3 sMc3 hcs bs 0 (emptyA [0 .. n - 2]) g
+      -- Do not reuse the initial generator.
+      gm <- newIOGenM $ head gs
+      return $ MC3 sMc3 hcs bs 0 (emptyA [0 .. n - 2]) gm
   where
     n = fromNChains $ mc3NChains sMc3
     sp = fromSwapPeriod $ mc3SwapPeriod sMc3
@@ -416,16 +414,13 @@
   where
     g = mc3Generator a
 
-mc3IsInValidState :: ToJSON a => MC3 a -> Bool
-mc3IsInValidState a = V.any aIsInValidState mhgs
+mc3IsInvalidState :: ToJSON a => MC3 a -> Bool
+mc3IsInvalidState a = V.any aIsInvalidState mhgs
   where
     mhgs = mc3MHGChains a
 
--- TODO (medium): Splitmix. 'mc3Iterate' is actually not parallel, but
--- concurrent because of the IO constraint. Use pure parallel code when we have
--- a pure generator.
---
--- However, we have to take care of the mutable traces.
+-- NOTE: 'mc3Iterate' is actually not parallel, but concurrent because of the IO
+-- constraint of the mutable trace.
 mc3Iterate ::
   ToJSON a =>
   IterationMode ->
diff --git a/src/Mcmc/Algorithm/MHG.hs b/src/Mcmc/Algorithm/MHG.hs
--- a/src/Mcmc/Algorithm/MHG.hs
+++ b/src/Mcmc/Algorithm/MHG.hs
@@ -61,7 +61,7 @@
 instance ToJSON a => Algorithm (MHG a) where
   aName = const "Metropolis-Hastings-Green (MHG)"
   aIteration = iteration . fromMHG
-  aIsInValidState = mhgIsInValidState
+  aIsInvalidState = mhgIsInvalidState
   aIterate = mhgIterate
   aAutoTune = mhgAutoTune
   aResetAcceptance = mhgResetAcceptance
@@ -73,6 +73,9 @@
   aCloseMonitors = mhgCloseMonitors
   aSave = mhgSave
 
+-- Calculate required length of trace. The length may be larger during burn in,
+-- because the tuners of some proposals (e.g., HMC, NUTS) require the states of
+-- the last tuning interval.
 getTraceLength ::
   Maybe BurnInSettings ->
   TraceLength ->
@@ -101,13 +104,14 @@
   Cycle a ->
   Monitor a ->
   InitialState a ->
-  IOGenM StdGen ->
+  StdGen ->
   IO (MHG a)
 mhg s pr lh cc mn i0 g = do
   -- The trace is a mutable vector and the mutable state needs to be handled by
   -- a monad.
   tr <- replicateT tl l0
-  return $ MHG $ Chain Nothing l0 0 tr ac g 0 pr lh cc mn
+  gm <- newIOGenM g
+  return $ MHG $ Chain Nothing l0 0 tr ac gm 0 pr lh cc mn
   where
     l0 = Link i0 (pr i0) (lh i0)
     ac = emptyA $ ccProposals cc
@@ -280,8 +284,8 @@
 --
 -- At the moment this just checks whether the prior, likelihood, or posterior
 -- are NaN or infinite.
-mhgIsInValidState :: MHG a -> Bool
-mhgIsInValidState a = checkSoft p || check l || check (p * l)
+mhgIsInvalidState :: MHG a -> Bool
+mhgIsInvalidState a = checkSoft p || check l || check (p * l)
   where
     x = link $ fromMHG a
     p = prior x
diff --git a/src/Mcmc/Chain/Trace.hs b/src/Mcmc/Chain/Trace.hs
--- a/src/Mcmc/Chain/Trace.hs
+++ b/src/Mcmc/Chain/Trace.hs
@@ -27,6 +27,9 @@
 import qualified Data.Vector as VB
 import Mcmc.Chain.Link
 
+-- NOTE: We directly refer to the 'PrimSate' 'RealWorld' because, otherwise, we
+-- have two type variables in 'Chain m a'.
+
 -- | A 'Trace' is a mutable circular stack that passes through a list of states
 -- with associated priors and likelihoods called 'Link's.
 newtype Trace a = Trace {fromTrace :: C.MStack VB.Vector RealWorld (Link a)}
diff --git a/src/Mcmc/Internal/Shuffle.hs b/src/Mcmc/Internal/Shuffle.hs
--- a/src/Mcmc/Internal/Shuffle.hs
+++ b/src/Mcmc/Internal/Shuffle.hs
@@ -28,8 +28,8 @@
 -- cleaner, in my opinion. However, I would like to move away from MWC so I
 -- leave the custom implementation for now.
 --
--- NOTE: Moving away from MWC is not anymore true because I can use SplitMix
--- with it.
+-- NOTE: I do not need to move away from MWC anymore true because I can use
+-- SplitMix with it.
 
 -- | Shuffle a vector.
 shuffle :: StatefulGen g m => [a] -> g -> m [a]
diff --git a/src/Mcmc/MarginalLikelihood.hs b/src/Mcmc/MarginalLikelihood.hs
--- a/src/Mcmc/MarginalLikelihood.hs
+++ b/src/Mcmc/MarginalLikelihood.hs
@@ -223,7 +223,7 @@
   Cycle a ->
   Monitor a ->
   a ->
-  IOGenM StdGen ->
+  StdGen ->
   -- For each point a vector of likelihoods stored in log domain.
   ML [VU.Vector Likelihood]
 mlRun k xs em vb prf lhf cc mn i0 g = do
@@ -270,12 +270,11 @@
   Cycle a ->
   Monitor a ->
   a ->
-  IOGenM StdGen ->
+  StdGen ->
   ML MarginalLikelihood
-tiWrapper s prf lhf cc mn i0 g0 = do
+tiWrapper s prf lhf cc mn i0 g = do
   logInfoB "Path integral (thermodynamic integration)."
-  r1 <- splitGenM g0
-  g1 <- newIOGenM r1
+  let (g0, g1) = split g
 
   -- Parallel execution of both path integrals.
   r <- ask
@@ -354,7 +353,7 @@
   Cycle a ->
   Monitor a ->
   a ->
-  IOGenM StdGen ->
+  StdGen ->
   ML MarginalLikelihood
 sssWrapper s prf lhf cc mn i0 g = do
   logInfoB "Stepping stone sampling."
@@ -378,7 +377,7 @@
   Cycle a ->
   Monitor a ->
   InitialState a ->
-  IOGenM StdGen ->
+  StdGen ->
   IO MarginalLikelihood
 marginalLikelihood s prf lhf cc mn i0 g = do
   -- Initialize.
diff --git a/src/Mcmc/Mcmc.hs b/src/Mcmc/Mcmc.hs
--- a/src/Mcmc/Mcmc.hs
+++ b/src/Mcmc/Mcmc.hs
@@ -31,7 +31,6 @@
 import Mcmc.Logger
 import Mcmc.Proposal (TuningType (LastTuningStep, NormalTuningStep))
 import Mcmc.Settings
-import System.Exit
 import System.IO
 import Prelude hiding (cycle)
 
@@ -109,7 +108,7 @@
   logInfoB "Initial state."
   logInfoB $ aStdMonitorHeader a
   mcmcExecuteMonitors a
-  when (aIsInValidState a) (logWarnB "The initial state is invalid!")
+  when (aIsInvalidState a) (logWarnB "The initial state is invalid!")
   a' <- mcmcBurnIn a
   logInfoS $ "Clean chain after burn in."
   let tl = sTraceLength s
diff --git a/src/Mcmc/Proposal.hs b/src/Mcmc/Proposal.hs
--- a/src/Mcmc/Proposal.hs
+++ b/src/Mcmc/Proposal.hs
@@ -199,8 +199,8 @@
     -- the ratio of the backward to forward kernels (the 'KernelRatio' or the
     -- probability masses or probability densities) and the 'Jacobian'.
     --
-    -- NOTE: Actually the 'Jacobian' should be part of the 'KernelRatio'. However,
-    -- it is more declarative to have them separate. Like so, we are constantly
+    -- Note: The 'Jacobian' should be part of the 'KernelRatio'. However, it is
+    -- more declarative to have them separate. Like so, we are constantly
     -- reminded: Is the Jacobian modifier different from 1.0?
     Propose !a !KernelRatio !Jacobian
   deriving (Show, Eq)
diff --git a/test/Mcmc/SaveSpec.hs b/test/Mcmc/SaveSpec.hs
--- a/test/Mcmc/SaveSpec.hs
+++ b/test/Mcmc/SaveSpec.hs
@@ -66,7 +66,7 @@
   describe "save and load" $
     it "doesn't change the MCMC chain" $
       do
-        gen <- newIOGenM $ mkStdGen 0
+        let gen = mkStdGen 0
         a <- mhg settings noPrior lh proposals mon 0 gen
         c <- fromMHG <$> mcmc settings a
         savedChain <- toSavedChain c
@@ -95,12 +95,11 @@
   describe "mhContinue" $
     it "mcmc 50 + mcmcContinue 50 == mcmc 100" $
       do
-        gen1 <- newIOGenM $ mkStdGen 0
-        a1 <- mhg settings noPrior lh proposals mon 0 gen1
+        let gen = mkStdGen 0
+        a1 <- mhg settings noPrior lh proposals mon 0 gen
         r1 <- fromMHG <$> mcmc settings a1
-        gen2 <- newIOGenM $ mkStdGen 0
         let settings' = settings {sIterations = Iterations 50}
-        a2 <- mhg settings' noPrior lh proposals mon 0 gen2
+        a2 <- mhg settings' noPrior lh proposals mon 0 gen
         r2' <- mcmc settings' a2
         r2 <- fromMHG <$> mcmcContinue (Iterations 50) settings' r2'
         link r1 `shouldBe` link r2