diff --git a/core/streamly-core.cabal b/core/streamly-core.cabal
index 8b4350f48d..a93f26926c 100644
--- a/core/streamly-core.cabal
+++ b/core/streamly-core.cabal
@@ -312,6 +312,8 @@ library
                      , Streamly.Internal.Data.Stream.StreamD
                      , Streamly.Internal.Data.Stream.Common
                      , Streamly.Internal.Data.Stream
+                     --, Streamly.Internal.Data.Stream.Cross
+                     --, Streamly.Internal.Data.Stream.Type
 
                      , Streamly.Internal.Data.Parser.ParserD.Tee
 
diff --git a/test/Streamly/Test/Data/Stream/Concurrent.hs b/test/Streamly/Test/Data/Stream/Concurrent.hs
index 9ed9237ea3..7fcbabb95c 100644
--- a/test/Streamly/Test/Data/Stream/Concurrent.hs
+++ b/test/Streamly/Test/Data/Stream/Concurrent.hs
@@ -17,17 +17,20 @@ import Control.Monad (replicateM)
 import Control.Monad.Catch (throwM)
 import Data.List (sort)
 import Data.Word (Word8)
-import Streamly.Data.Stream (Stream)
+import Streamly.Internal.Data.Stream (Stream)
+import Streamly.Internal.Data.Stream (mkCross, unCross)
 import Test.Hspec.QuickCheck
 import Test.QuickCheck (Testable, Property, choose, forAll, withMaxSuccess)
 import Test.QuickCheck.Monadic (monadicIO, run)
 import Test.Hspec as H
 
-import qualified Streamly.Data.Fold as Fold ( toList )
-import qualified Streamly.Data.Stream as Stream
-    ( replicate, fromEffect, fromPure, fromList, fold, take, nil )
 import qualified Streamly.Internal.Data.Stream.Concurrent as Async
 
+import qualified Streamly.Data.Fold as Fold
+import qualified Streamly.Data.Stream as Stream
+import qualified Streamly.Internal.Data.Stream as IS
+import qualified Streamly.Internal.Data.StreamK as K
+
 import Streamly.Test.Common (listEquals)
 
 moduleName :: String
@@ -218,6 +221,68 @@ sequenceReplicate cfg = constructWithLenM stream list
     list = flip replicateM (return 1 :: IO Int)
     stream = Async.parSequence cfg . flip Stream.replicate (return 1 :: IO Int)
 
+constructWithCons ::
+       Word8
+    -> (Async.Config -> Async.Config)
+    -> Property
+constructWithCons len cfg =
+    withMaxSuccess maxTestCount $
+    monadicIO $ do
+        strm <-
+            run
+               $ Stream.toList . Async.parEval cfg . Stream.take (fromIntegral len)
+               $ IS.fromStreamK
+               $ foldr K.cons K.nil (repeat (0::Int))
+        let list = replicate (fromIntegral len) 0
+        listEquals (==) strm list
+
+constructWithConsM ::
+       Word8
+    -> (Async.Config -> Async.Config)
+    -> Property
+constructWithConsM len cfg =
+    withMaxSuccess maxTestCount $
+    monadicIO $ do
+        strm <-
+            run
+               $ Stream.toList . Async.parEval cfg . Stream.take (fromIntegral len)
+               $ IS.fromStreamK
+               $ foldr K.consM K.nil (repeat (return (0::Int)))
+        let list = replicate (fromIntegral len) 0
+        listEquals (==) strm list
+
+monadBind ::
+       ([Int], [Int])
+    -> (Async.Config -> Async.Config)
+    -> Property
+monadBind (a, b) cfg =
+    withMaxSuccess maxTestCount $
+    monadicIO $ do
+        let st =  (mkCross $ Stream.fromList a)
+                    >>= \x -> (+ x) <$> (mkCross $ Stream.fromList b)
+        strm <- run
+                ((Stream.toList . Async.parEval cfg . unCross ) st)
+
+        let list = a >>= \x -> (+ x) <$> b
+        listEquals (==) strm list
+
+monadThen ::
+       ([Int], [Int])
+    -> (Async.Config -> Async.Config)
+    -> Property
+monadThen (a, b) cfg =
+    withMaxSuccess maxTestCount $
+    monadicIO $ do
+
+        let st =  (mkCross $ (Stream.fromList a :: IS.Stream IO Int))
+                    >> (mkCross $ Stream.fromList b)
+        strm <- run
+                ((Stream.toList . Async.parEval cfg . unCross ) st)
+
+        let list = a >> b
+        listEquals (==) strm list
+
+
 main :: IO ()
 main = hspec
   $ H.parallel
@@ -227,10 +292,14 @@ main = hspec
   $ describe moduleName $ do
         let transform = transformCombineFromList Stream.fromList sortEq
 
-        prop "parEval" $
-            transform
-                (fmap (+2))
-                (fmap (+1) . Async.parEval id . fmap (+1))
+        asyncSpec $
+            let appWith cfg = (fmap (+1) . Async.parEval cfg . fmap (+1))
+            in prop "parEval" . transform (fmap (+2)) . appWith
+
+        asyncSpec $ prop "constructWithCons" . constructWithCons 100
+        asyncSpec $ prop "constructWithConsM" . constructWithConsM 100
+        asyncSpec $ prop "monadBind" . monadBind ([1..100] , [1..100])
+        asyncSpec $ prop "monadThen" . monadThen ([1..100] , [1..100])
 
         asyncSpec $ prop "parSequence" . sequenceReplicate