diff --git a/call.go b/call.go
index d6326ea0..27cf6411 100644
--- a/call.go
+++ b/call.go
@@ -179,7 +179,10 @@ func Invoke(ctx context.Context, method string, args, reply interface{}, cc *Cli
 				put()
 				put = nil
 			}
-			if _, ok := err.(transport.ConnectionError); ok {
+			// Retry a non-failfast RPC when
+			// i) there is a connection error; or
+			// ii) the server started to drain before this RPC was initiated.
+			if _, ok := err.(transport.ConnectionError); ok || err == transport.ErrStreamDrain {
 				if c.failFast {
 					return toRPCErr(err)
 				}
diff --git a/clientconn.go b/clientconn.go
index 33edfa31..3206d674 100644
--- a/clientconn.go
+++ b/clientconn.go
@@ -697,14 +697,21 @@ func (ac *addrConn) tearDown(err error) {
 		}
 		ac.cc.mu.Unlock()
 	}()
-	if ac.state == Shutdown {
-		return
-	}
-	ac.state = Shutdown
 	if ac.down != nil {
 		ac.down(downErrorf(false, false, "%v", err))
 		ac.down = nil
 	}
+	if err == errConnDrain && ac.transport != nil {
+		// GracefulClose(...) may be executed multiple times when
+		// i) receiving multiple GoAway frames from the server; or
+		// ii) there are concurrent name resolver/Balancer triggered
+		// address removal and GoAway.
+		ac.transport.GracefulClose()
+	}
+	if ac.state == Shutdown {
+		return
+	}
+	ac.state = Shutdown
 	ac.stateCV.Broadcast()
 	if ac.events != nil {
 		ac.events.Finish()
@@ -714,12 +721,8 @@ func (ac *addrConn) tearDown(err error) {
 		close(ac.ready)
 		ac.ready = nil
 	}
-	if ac.transport != nil {
-		if err == errConnDrain {
-			ac.transport.GracefulClose()
-		} else {
-			ac.transport.Close()
-		}
+	if ac.transport != nil && err != errConnDrain {
+		ac.transport.Close()
 	}
 	if ac.shutdownChan != nil {
 		close(ac.shutdownChan)
diff --git a/server.go b/server.go
index 2ad331e1..1a250c79 100644
--- a/server.go
+++ b/server.go
@@ -795,12 +795,16 @@ func (s *Server) Stop() {
 // connections and RPCs and blocks until all the pending RPCs are finished.
 func (s *Server) GracefulStop() {
 	s.mu.Lock()
+	if s.drain == true || s.conns == nil {
+		s.mu.Lock()
+		return
+	}
 	s.drain = true
 	for lis := range s.lis {
 		lis.Close()
 	}
 	for c := range s.conns {
-		c.(transport.ServerTransport).GoAway()
+		c.(transport.ServerTransport).Drain()
 	}
 	for len(s.conns) != 0 {
 		s.cv.Wait()
diff --git a/test/end2end_test.go b/test/end2end_test.go
index a3f022a1..2cc4ccfc 100644
--- a/test/end2end_test.go
+++ b/test/end2end_test.go
@@ -2114,6 +2114,7 @@ func interestingGoroutines() (gs []string) {
 
 		if stack == "" ||
 			strings.Contains(stack, "testing.Main(") ||
+			strings.Contains(stack, "testing.tRunner(") ||
 			strings.Contains(stack, "runtime.goexit") ||
 			strings.Contains(stack, "created by runtime.gc") ||
 			strings.Contains(stack, "created by google3/base/go/log.init") ||
diff --git a/transport/handler_server.go b/transport/handler_server.go
index 35ccf627..3d7b15e5 100644
--- a/transport/handler_server.go
+++ b/transport/handler_server.go
@@ -370,8 +370,8 @@ func (ht *serverHandlerTransport) runStream() {
 	}
 }
 
-func (ht *serverHandlerTransport) GoAway() {
-	panic("not implemented")
+func (ht *serverHandlerTransport) Drain() {
+	panic("Drain() is not implemented")
 }
 
 // mapRecvMsgError returns the non-nil err into the appropriate
diff --git a/transport/http2_client.go b/transport/http2_client.go
index 20eb4bab..ffde50ae 100644
--- a/transport/http2_client.go
+++ b/transport/http2_client.go
@@ -102,6 +102,8 @@ type http2Client struct {
 	streamSendQuota uint32
 	// goAwayID records the Last-Stream-ID in the GoAway frame from the server.
 	goAwayID uint32
+	// prevGoAway ID records the Last-Stream-ID in the previous GOAway frame.
+	prevGoAwayID uint32
 }
 
 // newHTTP2Client constructs a connected ClientTransport to addr based on HTTP2
@@ -483,21 +485,25 @@ func (t *http2Client) GracefulClose() error {
 		t.mu.Unlock()
 		return nil
 	}
-	if t.state == draining {
-		t.mu.Unlock()
-		return nil
-	}
-	t.state = draining
 	// Notify the streams which were initiated after the server sent GOAWAY.
 	select {
 	case <-t.goAway:
-		for i := t.goAwayID + 2; i < t.nextID; i += 2 {
+		n := t.prevGoAwayID
+		if n == 0 && t.nextID > 1 {
+			n = t.nextID - 2
+		}
+		for i := t.goAwayID + 2; i <= n; i += 2 {
 			if s, ok := t.activeStreams[i]; ok {
 				close(s.goAway)
 			}
 		}
 	default:
 	}
+	if t.state == draining {
+		t.mu.Unlock()
+		return nil
+	}
+	t.state = draining
 	active := len(t.activeStreams)
 	t.mu.Unlock()
 	if active == 0 {
@@ -742,9 +748,21 @@ func (t *http2Client) handlePing(f *http2.PingFrame) {
 
 func (t *http2Client) handleGoAway(f *http2.GoAwayFrame) {
 	t.mu.Lock()
-	if t.state == reachable {
+	if t.state == reachable || t.state == draining {
+		if t.goAwayID > 0 && t.goAwayID < f.LastStreamID {
+			id := t.goAwayID
+			t.mu.Unlock()
+			t.notifyError(ConnectionErrorf("received illegal http2 GOAWAY frame: previously recv GOAWAY frame with LastStramID %d, currently recv %d", id, f.LastStreamID))
+			return
+		}
+		t.prevGoAwayID = t.goAwayID
 		t.goAwayID = f.LastStreamID
-		close(t.goAway)
+		select {
+		case <-t.goAway:
+			// t.goAway has been closed (i.e.,multiple GoAways).
+		default:
+			close(t.goAway)
+		}
 	}
 	t.mu.Unlock()
 }
diff --git a/transport/http2_server.go b/transport/http2_server.go
index f0d1f7f6..42f5d9c4 100644
--- a/transport/http2_server.go
+++ b/transport/http2_server.go
@@ -755,6 +755,6 @@ func (t *http2Server) RemoteAddr() net.Addr {
 	return t.conn.RemoteAddr()
 }
 
-func (t *http2Server) GoAway() {
+func (t *http2Server) Drain() {
 	t.controlBuf.put(&goAway{})
 }
diff --git a/transport/transport.go b/transport/transport.go
index f94731ed..9dade654 100644
--- a/transport/transport.go
+++ b/transport/transport.go
@@ -473,8 +473,8 @@ type ServerTransport interface {
 	// RemoteAddr returns the remote network address.
 	RemoteAddr() net.Addr
 
-	// GoAway notifies the client this ServerTransport stops accepting new RPCs.
-	GoAway()
+	// Drain notifies the client this ServerTransport stops accepting new RPCs.
+	Drain()
 }
 
 // StreamErrorf creates an StreamError with the specified error code and description.