diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,3 +1,7 @@
+# 1.0.6
+
+* Add `peekForeverE` combinator
+
 # 1.0.5
 
 * Add head, headDef and lastDef combinators
diff --git a/Data/Conduit/Combinators.hs b/Data/Conduit/Combinators.hs
--- a/Data/Conduit/Combinators.hs
+++ b/Data/Conduit/Combinators.hs
@@ -190,6 +190,7 @@
     , vectorBuilder
     , mapAccumS
     , peekForever
+    , peekForeverE
     ) where
 
 -- BEGIN IMPORTS
@@ -2148,6 +2149,27 @@
   where
     loop = do
         mx <- peek
+        case mx of
+            Nothing -> return ()
+            Just _ -> inner >> loop
+
+-- | Run a consuming conduit repeatedly, only stopping when there is no more
+-- data available from upstream.
+--
+-- In contrast to 'peekForever', this function will ignore empty
+-- chunks of data. So for example, if a stream of data contains an
+-- empty @ByteString@, it is still treated as empty, and the consuming
+-- function is not called.
+--
+-- @since 1.0.6
+peekForeverE :: (Monad m, MonoFoldable i)
+             => ConduitM i o m ()
+             -> ConduitM i o m ()
+peekForeverE inner =
+    loop
+  where
+    loop = do
+        mx <- peekE
         case mx of
             Nothing -> return ()
             Just _ -> inner >> loop
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
@@ -174,6 +174,7 @@
     , vectorBuilderC
     , CC.mapAccumS
     , CC.peekForever
+    , CC.peekForeverE
     ) where
 
 -- BEGIN IMPORTS
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:             1.0.5
+version:             1.0.6
 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/snoyberg/mono-traversable
diff --git a/test/Spec.hs b/test/Spec.hs
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -668,6 +668,10 @@
         res1 <- yieldMany strs $$ linesUnboundedC =$ sinkList
         res2 <- yieldMany strs $$ peekForever (lineC $ foldC >>= yield) =$ sinkList
         res2 `shouldBe` res1
+    prop "peekForeverE" $ \(strs :: [String]) -> do
+        res1 <- yieldMany strs $$ linesUnboundedC =$ sinkList
+        res2 <- yieldMany strs $$ peekForeverE (lineC $ foldC >>= yield) =$ sinkList
+        res2 `shouldBe` res1
     StreamSpec.spec
 
 evenInt :: Int -> Bool