diff --git a/h2.go b/h2.go
index 2f6342c7..7f559459 100644
--- a/h2.go
+++ b/h2.go
@@ -33,15 +33,28 @@ func (r *H2Transport) RoundTrip(_ *http.Request) (*http.Response, error) {
 	if !strings.Contains(raddr, ":") {
 		raddr += ":443"
 	}
+	serverName := r.Host
+	if host, _, err := net.SplitHostPort(raddr); err == nil {
+		serverName = host
+	}
 	rawServerTLS, err := dial("tcp", raddr)
 	if err != nil {
 		return nil, err
 	}
 	defer rawServerTLS.Close()
+	cfg := r.TLSConfig
+	if cfg != nil {
+		cfg = cfg.Clone()
+	} else {
+		cfg = &tls.Config{}
+	}
 	// Ensure that we only advertise HTTP/2 as the accepted protocol.
-	r.TLSConfig.NextProtos = []string{http2.NextProtoTLS}
+	cfg.NextProtos = []string{http2.NextProtoTLS}
+	if cfg.ServerName == "" {
+		cfg.ServerName = serverName
+	}
 	// Initiate TLS and check remote host name against certificate.
-	rawServerTLS = tls.Client(rawServerTLS, r.TLSConfig)
+	rawServerTLS = tls.Client(rawServerTLS, cfg)
 	rawTLSConn, ok := rawServerTLS.(*tls.Conn)
 	if !ok {
 		return nil, errors.New("invalid TLS connection")
@@ -49,8 +62,8 @@ func (r *H2Transport) RoundTrip(_ *http.Request) (*http.Response, error) {
 	if err = rawTLSConn.HandshakeContext(context.Background()); err != nil {
 		return nil, err
 	}
-	if r.TLSConfig == nil || !r.TLSConfig.InsecureSkipVerify {
-		if err = rawTLSConn.VerifyHostname(raddr[:strings.LastIndex(raddr, ":")]); err != nil {
+	if !cfg.InsecureSkipVerify {
+		if err = rawTLSConn.VerifyHostname(serverName); err != nil {
 			return nil, err
 		}
 	}