diff --git a/http2/server.go b/http2/server.go
index 0e670de..54655a5 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -2,17 +2,6 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
-// TODO: replace all <-sc.doneServing with reads from the stream's cw
-// instead, and make sure that on close we close all open
-// streams. then remove doneServing?
-
-// TODO: re-audit GOAWAY support. Consider each incoming frame type and
-// whether it should be ignored during graceful shutdown.
-
-// TODO: disconnect idle clients. GFE seems to do 4 minutes. make
-// configurable?  or maximum number of idle clients and remove the
-// oldest?
-
 // TODO: turn off the serve goroutine when idle, so
 // an idle conn only has the readFrames goroutine active. (which could
 // also be optimized probably to pin less memory in crypto/tls). This
@@ -114,6 +103,11 @@
 	// PermitProhibitedCipherSuites, if true, permits the use of
 	// cipher suites prohibited by the HTTP/2 spec.
 	PermitProhibitedCipherSuites bool
+
+	// IdleTimeout specifies how long until idle clients should be
+	// closed with a GOAWAY frame. PING frames are not considered
+	// activity for the purposes of IdleTimeout.
+	IdleTimeout time.Duration
 }
 
 func (s *Server) maxReadFrameSize() uint32 {
@@ -390,6 +384,8 @@
 	goAwayCode            ErrCode
 	shutdownTimerCh       <-chan time.Time // nil until used
 	shutdownTimer         *time.Timer      // nil until used
+	idleTimer             *time.Timer      // nil if unused
+	idleTimerCh           <-chan time.Time // nil if unused
 
 	// Owned by the writeFrameAsync goroutine:
 	headerWriteBuf bytes.Buffer
@@ -681,6 +677,12 @@
 	sc.setConnState(http.StateActive)
 	sc.setConnState(http.StateIdle)
 
+	if sc.srv.IdleTimeout != 0 {
+		sc.idleTimer = time.NewTimer(sc.srv.IdleTimeout)
+		defer sc.idleTimer.Stop()
+		sc.idleTimerCh = sc.idleTimer.C
+	}
+
 	go sc.readFrames() // closed by defer sc.conn.Close above
 
 	settingsTimer := time.NewTimer(firstSettingsTimeout)
@@ -709,6 +711,9 @@
 		case <-sc.shutdownTimerCh:
 			sc.vlogf("GOAWAY close timer fired; closing conn from %v", sc.conn.RemoteAddr())
 			return
+		case <-sc.idleTimerCh:
+			sc.vlogf("connection is idle")
+			sc.goAway(ErrCodeNo)
 		case fn := <-sc.testHookCh:
 			fn(loopNum)
 		}
@@ -1114,12 +1119,18 @@
 		// PROTOCOL_ERROR."
 		return ConnectionError(ErrCodeProtocol)
 	}
+	if sc.inGoAway {
+		return nil
+	}
 	sc.writeFrame(frameWriteMsg{write: writePingAck{f}})
 	return nil
 }
 
 func (sc *serverConn) processWindowUpdate(f *WindowUpdateFrame) error {
 	sc.serveG.check()
+	if sc.inGoAway {
+		return nil
+	}
 	switch {
 	case f.StreamID != 0: // stream-level flow control
 		state, st := sc.state(f.StreamID)
@@ -1152,6 +1163,9 @@
 
 func (sc *serverConn) processResetStream(f *RSTStreamFrame) error {
 	sc.serveG.check()
+	if sc.inGoAway {
+		return nil
+	}
 
 	state, st := sc.state(f.StreamID)
 	if state == stateIdle {
@@ -1181,6 +1195,9 @@
 		sc.setConnState(http.StateIdle)
 	}
 	delete(sc.streams, st.id)
+	if len(sc.streams) == 0 && sc.srv.IdleTimeout != 0 {
+		sc.idleTimer.Reset(sc.srv.IdleTimeout)
+	}
 	if p := st.body; p != nil {
 		// Return any buffered unread bytes worth of conn-level flow control.
 		// See golang.org/issue/16481
@@ -1204,6 +1221,9 @@
 		}
 		return nil
 	}
+	if sc.inGoAway {
+		return nil
+	}
 	if err := f.ForeachSetting(sc.processSetting); err != nil {
 		return err
 	}
@@ -1275,6 +1295,9 @@
 
 func (sc *serverConn) processData(f *DataFrame) error {
 	sc.serveG.check()
+	if sc.inGoAway {
+		return nil
+	}
 	data := f.Data()
 
 	// "If a DATA frame is received whose stream is not in "open"
@@ -1412,6 +1435,10 @@
 	}
 	sc.maxStreamID = id
 
+	if sc.idleTimer != nil {
+		sc.idleTimer.Stop()
+	}
+
 	ctx, cancelCtx := contextWithCancel(sc.baseCtx)
 	st = &stream{
 		sc:        sc,
@@ -1524,6 +1551,9 @@
 }
 
 func (sc *serverConn) processPriority(f *PriorityFrame) error {
+	if sc.inGoAway {
+		return nil
+	}
 	adjustStreamPriority(sc.streams, f.StreamID, f.PriorityParam)
 	return nil
 }
diff --git a/http2/server_test.go b/http2/server_test.go
index 31d12f2..e7309b9 100644
--- a/http2/server_test.go
+++ b/http2/server_test.go
@@ -86,12 +86,15 @@
 	}
 
 	var onlyServer, quiet bool
+	h2server := new(Server)
 	for _, opt := range opts {
 		switch v := opt.(type) {
 		case func(*tls.Config):
 			v(tlsConfig)
 		case func(*httptest.Server):
 			v(ts)
+		case func(*Server):
+			v(h2server)
 		case serverTesterOpt:
 			switch v {
 			case optOnlyServer:
@@ -106,7 +109,7 @@
 		}
 	}
 
-	ConfigureServer(ts.Config, &Server{})
+	ConfigureServer(ts.Config, h2server)
 
 	st := &serverTester{
 		t:      t,
@@ -3406,6 +3409,52 @@
 
 }
 
+func TestServerIdleTimeout(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping in short mode")
+	}
+
+	st := newServerTester(t, func(w http.ResponseWriter, r *http.Request) {
+	}, func(h2s *Server) {
+		h2s.IdleTimeout = 500 * time.Millisecond
+	})
+	defer st.Close()
+
+	st.greet()
+	ga := st.wantGoAway()
+	if ga.ErrCode != ErrCodeNo {
+		t.Errorf("GOAWAY error = %v; want ErrCodeNo", ga.ErrCode)
+	}
+}
+
+func TestServerIdleTimeout_AfterRequest(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping in short mode")
+	}
+	const timeout = 250 * time.Millisecond
+
+	st := newServerTester(t, func(w http.ResponseWriter, r *http.Request) {
+		time.Sleep(timeout * 2)
+	}, func(h2s *Server) {
+		h2s.IdleTimeout = timeout
+	})
+	defer st.Close()
+
+	st.greet()
+
+	// Send a request which takes twice the timeout. Verifies the
+	// idle timeout doesn't fire while we're in a request:
+	st.bodylessReq1()
+	st.wantHeaders()
+
+	// But the idle timeout should be rearmed after the request
+	// is done:
+	ga := st.wantGoAway()
+	if ga.ErrCode != ErrCodeNo {
+		t.Errorf("GOAWAY error = %v; want ErrCodeNo", ga.ErrCode)
+	}
+}
+
 // grpc-go closes the Request.Body currently with a Read.
 // Verify that it doesn't race.
 // See https://github.com/grpc/grpc-go/pull/938
diff --git a/http2/transport_test.go b/http2/transport_test.go
index f0af30a..2006a3d 100644
--- a/http2/transport_test.go
+++ b/http2/transport_test.go
@@ -1947,8 +1947,17 @@
 		},
 	}
 	for i, tt := range tests {
+		// Ignore the session ticket keys part, which ends up populating
+		// unexported fields in the Config:
+		if tt.conf != nil {
+			tt.conf.SessionTicketsDisabled = true
+		}
+
 		tr := &Transport{TLSClientConfig: tt.conf}
 		got := tr.newTLSConfig(tt.host)
+
+		got.SessionTicketsDisabled = false
+
 		if !reflect.DeepEqual(got, tt.want) {
 			t.Errorf("%d. got %#v; want %#v", i, got, tt.want)
 		}