diff --git a/http2/transport.go b/http2/transport.go
index 98a49c6b6..61f511f97 100644
--- a/http2/transport.go
+++ b/http2/transport.go
@@ -827,10 +827,6 @@ func (t *Transport) newClientConn(c net.Conn, singleUse bool) (*ClientConn, erro
 	cc.henc.SetMaxDynamicTableSizeLimit(t.maxEncoderHeaderTableSize())
 	cc.peerMaxHeaderTableSize = initialHeaderTableSize
 
-	if t.AllowHTTP {
-		cc.nextStreamID = 3
-	}
-
 	if cs, ok := c.(connectionStater); ok {
 		state := cs.ConnectionState()
 		cc.tlsState = &state
diff --git a/http2/transport_test.go b/http2/transport_test.go
index ddeaf6137..498e27932 100644
--- a/http2/transport_test.go
+++ b/http2/transport_test.go
@@ -5401,3 +5401,23 @@ func TestIssue66763Race(t *testing.T) {
 
 	<-donec
 }
+
+// Issue 67671: Sending a Connection: close request on a Transport with AllowHTTP
+// set caused a the transport to wedge.
+func TestIssue67671(t *testing.T) {
+	ts := newTestServer(t, func(w http.ResponseWriter, r *http.Request) {})
+	tr := &Transport{
+		TLSClientConfig: tlsConfigInsecure,
+		AllowHTTP:       true,
+	}
+	defer tr.CloseIdleConnections()
+	req, _ := http.NewRequest("GET", ts.URL, nil)
+	req.Close = true
+	for i := 0; i < 2; i++ {
+		res, err := tr.RoundTrip(req)
+		if err != nil {
+			t.Fatal(err)
+		}
+		res.Body.Close()
+	}
+}