diff --git a/clientv3/integration/lease_test.go b/clientv3/integration/lease_test.go
index a0c411826..ef176fddf 100644
--- a/clientv3/integration/lease_test.go
+++ b/clientv3/integration/lease_test.go
@@ -729,6 +729,12 @@ func TestLeaseWithRequireLeader(t *testing.T) {
 	}
 
 	clus.Members[1].Stop(t)
+	// kaReqLeader may issue multiple requests while waiting for the first
+	// response from proxy server; drain any stray keepalive responses
+	time.Sleep(100 * time.Millisecond)
+	for len(kaReqLeader) > 0 {
+		<-kaReqLeader
+	}
 
 	select {
 	case resp, ok := <-kaReqLeader:
diff --git a/integration/cluster_proxy.go b/integration/cluster_proxy.go
index 0152a16c6..8593b5064 100644
--- a/integration/cluster_proxy.go
+++ b/integration/cluster_proxy.go
@@ -75,6 +75,7 @@ type proxyCloser struct {
 	clientv3.Watcher
 	wdonec  <-chan struct{}
 	kvdonec <-chan struct{}
+	lclose  func()
 	lpdonec <-chan struct{}
 }
 
@@ -83,6 +84,7 @@ func (pc *proxyCloser) Close() error {
 	<-pc.kvdonec
 	err := pc.Watcher.Close()
 	<-pc.wdonec
+	pc.lclose()
 	<-pc.lpdonec
 	return err
 }
@@ -95,11 +97,13 @@ func newClientV3(cfg clientv3.Config) (*clientv3.Client, error) {
 	rpc := toGRPC(c)
 	c.KV = clientv3.NewKVFromKVClient(rpc.KV)
 	pmu.Lock()
+	lc := c.Lease
 	c.Lease = clientv3.NewLeaseFromLeaseClient(rpc.Lease, cfg.DialTimeout)
 	c.Watcher = &proxyCloser{
 		Watcher: clientv3.NewWatchFromWatchClient(rpc.Watch),
 		wdonec:  proxies[c].wdonec,
 		kvdonec: proxies[c].kvdonec,
+		lclose:  func() { lc.Close() },
 		lpdonec: proxies[c].lpdonec,
 	}
 	pmu.Unlock()