diff --git a/test/end2end_test.go b/test/end2end_test.go
index 11e215d7..0bbc3d90 100644
--- a/test/end2end_test.go
+++ b/test/end2end_test.go
@@ -566,12 +566,6 @@ func TestServerGoAway(t *testing.T) {
 func testServerGoAway(t *testing.T, e env) {
 	te := newTest(t, e)
 	te.userAgent = testAppUA
-	te.declareLogNoise(
-		"transport: http2Client.notifyError got notified that the client transport was broken EOF",
-		"grpc: Conn.transportMonitor exits due to: grpc: the client connection is closing",
-		"grpc: Conn.resetTransport failed to create client transport: connection error",
-		"grpc: Conn.resetTransport failed to create client transport: connection error: desc = \"transport: dial unix",
-	)
 	te.startServer(&testServer{security: e.security})
 	defer te.tearDown()
 
diff --git a/transport/http2_client.go b/transport/http2_client.go
index cf392b1c..6a34c7e5 100644
--- a/transport/http2_client.go
+++ b/transport/http2_client.go
@@ -496,7 +496,7 @@ func (t *http2Client) Close() (err error) {
 
 func (t *http2Client) GracefulClose() error {
 	t.mu.Lock()
-	if t.state == closing {
+	if t.state == closing || t.state == unreachable {
 		t.mu.Unlock()
 		return nil
 	}