diff --git a/stream.go b/stream.go
index fb7e50f9..008ad1e2 100644
--- a/stream.go
+++ b/stream.go
@@ -165,7 +165,7 @@ func NewClientStream(ctx context.Context, desc *StreamDesc, cc *ClientConn, meth
 				put()
 				put = nil
 			}
-			if _, ok := err.(transport.ConnectionError); ok {
+			if _, ok := err.(transport.ConnectionError); ok || err == transport.ErrStreamDrain {
 				if c.failFast {
 					cs.finish(err)
 					return nil, toRPCErr(err)
diff --git a/transport/http2_client.go b/transport/http2_client.go
index b6b744d5..6c72431a 100644
--- a/transport/http2_client.go
+++ b/transport/http2_client.go
@@ -284,6 +284,10 @@ func (t *http2Client) NewStream(ctx context.Context, callHdr *CallHdr) (_ *Strea
 		t.mu.Unlock()
 		return nil, ErrConnClosing
 	}
+	if t.state == draining {
+		t.mu.Unlock()
+		return nil, ErrStreamDrain
+	}
 	if t.state != reachable {
 		t.mu.Unlock()
 		return nil, ErrConnClosing
@@ -310,7 +314,6 @@ func (t *http2Client) NewStream(ctx context.Context, callHdr *CallHdr) (_ *Strea
 	t.mu.Lock()
 	if t.state == draining {
 		t.mu.Unlock()
-		// t has been drained. Return the quota.
 		t.streamsQuota.add(1)
 		// Need to make t writable again so that the rpc in flight can still proceed.
 		t.writableChan <- 0