diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,9 @@
 # ChangeLog for warp
 
+## 3.4.6
+
+* Using `withHandle` of time-manager.
+
 ## 3.4.5
 
 * Rethrowing asynchronous exceptions and preventing callsing
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
@@ -106,10 +106,6 @@
             logResponse req st msiz
             mapM_ (logPushPromise req) pps
         Left e
-          -- killed by the local worker manager
-          | 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
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
@@ -355,7 +355,7 @@
 
     -- We need to register a timeout handler for this thread, and
     -- cancel that handler as soon as we exit.
-    serve unmask (conn, transport) = E.bracket register cancel $ \th -> do
+    serve unmask (conn, transport) = T.withHandleKillThread (timeoutManager ii) (return ()) $ \th -> do
         -- We now have fully registered a connection close handler in
         -- the case of all exceptions, so it is safe to once again
         -- allow async exceptions.
@@ -368,9 +368,6 @@
                 -- Actually serve this connection.  bracket with closeConn
                 -- above ensures the connection is closed.
                 when goingon $ serveConnection conn ii th addr transport set app
-      where
-        register = T.registerKillThread (timeoutManager ii) (return ())
-        cancel = T.cancel
 
     onOpen adr = increase counter >> settingsOnOpen set adr
     onClose adr _ = decrease counter >> settingsOnClose set adr
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:            3.4.5
+version:            3.4.6
 license:            MIT
 license-file:       LICENSE
 maintainer:         michael@snoyman.com
@@ -102,7 +102,7 @@
         stm >=2.3,
         streaming-commons >=0.1.10,
         text,
-        time-manager >=0.1 && <0.2,
+        time-manager >=0.1.3 && <0.2,
         vault >=0.3,
         wai >=3.2.4 && <3.3,
         word8