diff --git a/rhine/rhine.cabal b/rhine/rhine.cabal
index 9ed57eb7..12624811 100644
--- a/rhine/rhine.cabal
+++ b/rhine/rhine.cabal
@@ -138,6 +138,7 @@ library
   other-modules:
     FRP.Rhine.ClSF.Except.Util
     FRP.Rhine.ClSF.Random.Util
+    FRP.Rhine.Schedule.Internal
 
   -- LANGUAGE extensions used by modules in this package.
   -- other-extensions:
@@ -146,6 +147,7 @@ library
     MonadRandom >=0.5,
     containers >=0.5,
     deepseq >=1.4,
+    foldable1-classes-compat ^>=0.1,
     free >=5.1,
     mmorph ^>=1.2,
     profunctors ^>=5.6,
diff --git a/rhine/src/FRP/Rhine/Schedule.hs b/rhine/src/FRP/Rhine/Schedule.hs
index e2784a6d..d2dbbbc4 100644
--- a/rhine/src/FRP/Rhine/Schedule.hs
+++ b/rhine/src/FRP/Rhine/Schedule.hs
@@ -20,22 +20,16 @@ module FRP.Rhine.Schedule where
 import Control.Arrow
 import Data.List.NonEmpty as N
 
--- transformers
-import Control.Monad.Trans.Reader
-
 -- monad-schedule
 import Control.Monad.Schedule.Class
 
 -- automaton
 import Data.Automaton
-import Data.Automaton.Recursive (getRecursive, toRecursive)
-import Data.Stream
 import Data.Stream.Optimized (OptimizedStreamT (..), toStreamT)
-import Data.Stream.Recursive qualified as StreamRecursive
-import Data.Stream.Result
 
 -- rhine
 import FRP.Rhine.Clock
+import FRP.Rhine.Schedule.Internal
 
 -- * Scheduling
 
@@ -48,35 +42,15 @@ scheduleList :: (Monad m, MonadSchedule m) => NonEmpty (Automaton m a b) -> Auto
 scheduleList automatons0 =
   Automaton $
     Stateful $
-      StreamT
-        { state = (getRecursive . toRecursive <$> automatons0, [])
-        , step = \(automatons, running) -> ReaderT $ \a -> do
-            let bsAndConts = flip (runReaderT . StreamRecursive.getRecursive) a <$> automatons
-            (done, running') <- schedule (N.head bsAndConts :| N.tail bsAndConts ++ running)
-            return $ Result (resultState <$> done, running') $ output <$> done
-        }
+      scheduleStreams' $
+        toStreamT . getAutomaton <$> automatons0
 
 {- | Run two automata concurrently.
 
 Whenever one automaton returns a value, it is returned.
-
-This is similar to 'scheduleList', but more efficient.
 -}
 schedulePair :: (Monad m, MonadSchedule m) => Automaton m a b -> Automaton m a b -> Automaton m a b
-schedulePair (Automaton automatonL) (Automaton automatonR) = Automaton $! Stateful $! scheduleStreams (toStreamT automatonL) (toStreamT automatonR)
-  where
-    scheduleStreams :: (Monad m, MonadSchedule m) => StreamT m b -> StreamT m b -> StreamT m b
-    scheduleStreams (StreamT stateL0 stepL) (StreamT stateR0 stepR) =
-      StreamT
-        { state = (stepL stateL0, stepR stateR0)
-        , step
-        }
-      where
-        step (runningL, runningR) = do
-          result <- race runningL runningR
-          case result of
-            Left (Result stateL' b, runningR') -> return $ Result (stepL stateL', runningR') b
-            Right (runningL', Result stateR' b) -> return $ Result (runningL', stepR stateR') b
+schedulePair automatonL automatonR = concatS $ fmap toList $ scheduleList $ automatonL :| [automatonR]
 
 -- | Run two running clocks concurrently.
 runningSchedule ::
diff --git a/rhine/src/FRP/Rhine/Schedule/Internal.hs b/rhine/src/FRP/Rhine/Schedule/Internal.hs
new file mode 100644
index 00000000..263fb446
--- /dev/null
+++ b/rhine/src/FRP/Rhine/Schedule/Internal.hs
@@ -0,0 +1,85 @@
+{-# LANGUAGE ExistentialQuantification #-}
+
+module FRP.Rhine.Schedule.Internal where
+
+-- base
+import Control.Arrow
+import Data.Function ((&))
+import Data.Functor ((<&>))
+import Data.Functor.Compose (Compose (..))
+import Data.Kind (Type)
+import Data.List.NonEmpty as N
+
+-- foldable1-classes-compat
+import Data.Foldable1 (Foldable1 (foldrMap1))
+
+-- sop-core
+import Data.SOP (HCollapse (hcollapse), HSequence (htraverse'), I (..), K (K), NP (..), NS (..), SListI, apInjs_NP, hliftA, hzipWith, unI)
+
+-- monad-schedule
+import Control.Monad.Schedule.Class
+
+-- automaton
+import Data.Stream hiding (concatS)
+import Data.Stream.Result
+
+-- | One step of a stream, with the state type argument going last, so it is usable with sop-core.
+newtype Step m b state = Step {getStep :: ResultStateT state m b}
+
+-- | The result of a stream, with the type arguments swapped, so it's usable with sop-core
+newtype RunningResult b state = RunningResult {getRunningResult :: Result state b}
+
+-- | Transform an n-ary product of at least one type into a nonempty list of all its content.
+apInjs_NPNonEmpty :: (SListI xs) => NP f (x ': xs) -> NonEmpty (NS f (x ': xs))
+apInjs_NPNonEmpty (fx :* fxs) = Z fx :| (S <$> apInjs_NP fxs)
+
+-- | A nonempty list of 'StreamT's, unzipped into their states and their steps.
+data Streams m b = forall state (states :: [Type]).
+  (SListI states) =>
+  Streams
+  { states :: NP I (state ': states)
+  , steps :: NP (Step m b) (state ': states)
+  }
+
+-- | Run 'Streams' concurrently by scheduling them in 'MonadSchedule'.
+scheduleStreams :: (MonadSchedule m, Functor m, Applicative m) => Streams m b -> StreamT m (NonEmpty b)
+scheduleStreams Streams {states, steps} =
+  StreamT
+    { state = (apInjs_NPNonEmpty states, []) -- All the initial states and no currently running continuations
+    , step =
+        -- Some streams have not started yet, or just finished their step. Others are still running.
+        \(restingStates, runningStreams) ->
+          -- Start all currently not running streams by zipping each with its step
+          fmap (htraverse' getCompose . hzipWith (\Step {getStep} -> Compose . fmap RunningResult . getResultStateT getStep . unI) steps) restingStates
+            -- Append all already running states to the freshly started ones
+            & flip appendList runningStreams
+            -- Schedule all running streams concurrently
+            & schedule
+            -- Separate into finished streams and still running streams
+            & fmap
+              ( \(finished, running) ->
+                  let finishedStates = finished <&> (hliftA (getRunningResult >>> resultState >>> I))
+                      outputs =
+                        finished
+                          <&> (hliftA (getRunningResult >>> output >>> K) >>> hcollapse)
+                   in Result (finishedStates, running) outputs
+              )
+    }
+
+-- | Run a nonempty list of streams concurrently.
+scheduleStreams' :: (MonadSchedule m, Applicative m) => NonEmpty (StreamT m b) -> StreamT m (NonEmpty b)
+scheduleStreams' = scheduleStreams . foldrMap1 buildStreams consStreams
+  where
+    buildStreams :: StreamT m b -> Streams m b
+    buildStreams StreamT {state, step} =
+      Streams
+        { states = I state :* Nil
+        , steps = Step (ResultStateT step) :* Nil
+        }
+
+    consStreams :: StreamT m b -> Streams m b -> Streams m b
+    consStreams StreamT {state, step} Streams {states, steps} =
+      Streams
+        { states = I state :* states
+        , steps = Step (ResultStateT step) :* steps
+        }