diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,11 @@
 # ChangeLog for warp
 
+## 3.4.5
+
+* Rethrowing asynchronous exceptions and preventing callsing
+  `connClose` twice.
+  [#1013](https://github.com/yesodweb/wai/pull/1013)
+
 ## 3.4.4
 
 * Removing `unliftio`.
diff --git a/Network/Wai/Handler/Warp/HTTP1.hs b/Network/Wai/Handler/Warp/HTTP1.hs
--- a/Network/Wai/Handler/Warp/HTTP1.hs
+++ b/Network/Wai/Handler/Warp/HTTP1.hs
@@ -122,6 +122,7 @@
         | Just NoKeepAliveRequest <- fromException e = return ()
         -- No valid request
         | Just (BadFirstLine _) <- fromException e = return ()
+        | isAsyncException e = throwIO e
         | otherwise = do
             _ <-
                 sendErrorResponse
@@ -204,6 +205,7 @@
         Right ResponseReceived -> return ()
         Left (e :: SomeException)
             | Just (ExceptionInsideResponseBody e') <- fromException e -> throwIO e'
+            | isAsyncException e -> throwIO e
             | otherwise -> do
                 keepAlive <- sendErrorResponse settings ii conn th istatus req e
                 settingsOnException settings (Just req) e
diff --git a/Network/Wai/Handler/Warp/HTTP2.hs b/Network/Wai/Handler/Warp/HTTP2.hs
--- a/Network/Wai/Handler/Warp/HTTP2.hs
+++ b/Network/Wai/Handler/Warp/HTTP2.hs
@@ -110,6 +110,7 @@
           | Just E.ThreadKilled  <- E.fromException e -> return ()
           -- killed by the local timeout manager
           | Just T.TimeoutThread <- E.fromException e -> return ()
+          | isAsyncException e -> E.throwIO e
           | otherwise -> do
             S.settingsOnException settings (Just req) e
             let ersp = S.settingsOnExceptionResponse settings e
@@ -152,7 +153,7 @@
     return bs
   where
     handler :: E.SomeException -> IO ByteString
-    handler _ = return ""
+    handler = throughAsync (return "")
 
 -- connClose must not be called here since Run:fork calls it
 goaway :: Connection -> H2.ErrorCodeId -> ByteString -> IO ()
diff --git a/Network/Wai/Handler/Warp/Imports.hs b/Network/Wai/Handler/Warp/Imports.hs
--- a/Network/Wai/Handler/Warp/Imports.hs
+++ b/Network/Wai/Handler/Warp/Imports.hs
@@ -10,9 +10,12 @@
     module Data.Word,
     module Data.Maybe,
     module Numeric,
+    throughAsync,
+    isAsyncException,
 ) where
 
 import Control.Applicative
+import Control.Exception
 import Control.Monad
 import Data.Bits
 import Data.ByteString.Internal (ByteString (..))
@@ -23,3 +26,14 @@
 import Data.Ord
 import Data.Word
 import Numeric
+
+isAsyncException :: Exception e => e -> Bool
+isAsyncException e =
+    case fromException (toException e) of
+        Just (SomeAsyncException _) -> True
+        Nothing -> False
+
+throughAsync :: IO a -> SomeException -> IO a
+throughAsync action (SomeException e)
+    | isAsyncException e = throwIO e
+    | otherwise = action
diff --git a/Network/Wai/Handler/Warp/Run.hs b/Network/Wai/Handler/Warp/Run.hs
--- a/Network/Wai/Handler/Warp/Run.hs
+++ b/Network/Wai/Handler/Warp/Run.hs
@@ -81,7 +81,7 @@
                             else settingsGracefulCloseTimeout1 set
                 if tm == 0
                     then close s
-                    else gracefulClose s tm `E.catch` \(E.SomeException _) -> return ()
+                    else gracefulClose s tm `E.catch` throughAsync (return ())
 #else
             , connClose = close s
 #endif
@@ -179,7 +179,7 @@
         (s, sa) <- accept' socket
         setSocketCloseOnExec s
         -- NoDelay causes an error for AF_UNIX.
-        setSocketOption s NoDelay 1 `E.catch` \(E.SomeException _) -> return ()
+        setSocketOption s NoDelay 1 `E.catch` throughAsync (return ())
         conn <- socketConnection set s
         return (conn, sa)
 
@@ -369,7 +369,7 @@
                 -- above ensures the connection is closed.
                 when goingon $ serveConnection conn ii th addr transport set app
       where
-        register = T.registerKillThread (timeoutManager ii) (connClose conn)
+        register = T.registerKillThread (timeoutManager ii) (return ())
         cancel = T.cancel
 
     onOpen adr = increase counter >> settingsOnOpen set adr
diff --git a/Network/Wai/Handler/Warp/Settings.hs b/Network/Wai/Handler/Warp/Settings.hs
--- a/Network/Wai/Handler/Warp/Settings.hs
+++ b/Network/Wai/Handler/Warp/Settings.hs
@@ -9,7 +9,7 @@
 
 module Network.Wai.Handler.Warp.Settings where
 
-import Control.Exception (SomeException, fromException)
+import Control.Exception (SomeException(..), fromException, throw)
 import qualified Data.ByteString.Builder as Builder
 import qualified Data.ByteString.Char8 as C8
 import Data.Streaming.Network (HostPreference)
@@ -17,7 +17,7 @@
 import qualified Data.Text.IO as TIO
 import Data.Version (showVersion)
 import GHC.IO (IO (IO), unsafeUnmask)
-import GHC.IO.Exception (AsyncException (ThreadKilled), IOErrorType (..))
+import GHC.IO.Exception (IOErrorType (..))
 import GHC.Prim (fork#)
 import qualified Network.HTTP.Types as H
 import Network.Socket (SockAddr, Socket, accept)
@@ -228,12 +228,11 @@
 -- Since 2.1.3
 defaultShouldDisplayException :: SomeException -> Bool
 defaultShouldDisplayException se
-    | Just ThreadKilled <- fromException se = False
     | Just (_ :: InvalidRequest) <- fromException se = False
     | Just (ioeGetErrorType -> et) <- fromException se
     , et == ResourceVanished || et == InvalidArgument =
         False
-    | Just TimeoutThread <- fromException se = False
+    | isAsyncException se = False
     | otherwise = True
 
 -- | Printing an exception to standard error
@@ -255,6 +254,7 @@
 -- Since 3.2.27
 defaultOnExceptionResponse :: SomeException -> Response
 defaultOnExceptionResponse e
+    | isAsyncException e = throw e
     | Just PayloadTooLarge <- fromException e =
         responseLBS
             H.status413
diff --git a/warp.cabal b/warp.cabal
--- a/warp.cabal
+++ b/warp.cabal
@@ -1,6 +1,6 @@
 cabal-version:      >=1.10
 name:               warp
-version:            3.4.4
+version:            3.4.5
 license:            MIT
 license-file:       LICENSE
 maintainer:         michael@snoyman.com