diff --git a/http2/go115.go b/http2/go115.go
new file mode 100644
index 0000000..908af1a
--- /dev/null
+++ b/http2/go115.go
@@ -0,0 +1,27 @@
+// Copyright 2021 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:build go1.15
+// +build go1.15
+
+package http2
+
+import (
+	"context"
+	"crypto/tls"
+)
+
+// dialTLSWithContext uses tls.Dialer, added in Go 1.15, to open a TLS
+// connection.
+func (t *Transport) dialTLSWithContext(ctx context.Context, network, addr string, cfg *tls.Config) (*tls.Conn, error) {
+	dialer := &tls.Dialer{
+		Config: cfg,
+	}
+	cn, err := dialer.DialContext(ctx, network, addr)
+	if err != nil {
+		return nil, err
+	}
+	tlsCn := cn.(*tls.Conn) // DialContext comment promises this will always succeed
+	return tlsCn, nil
+}
diff --git a/http2/not_go115.go b/http2/not_go115.go
new file mode 100644
index 0000000..e6c04cf
--- /dev/null
+++ b/http2/not_go115.go
@@ -0,0 +1,31 @@
+// Copyright 2021 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:build !go1.15
+// +build !go1.15
+
+package http2
+
+import (
+	"context"
+	"crypto/tls"
+)
+
+// dialTLSWithContext opens a TLS connection.
+func (t *Transport) dialTLSWithContext(ctx context.Context, network, addr string, cfg *tls.Config) (*tls.Conn, error) {
+	cn, err := tls.Dial(network, addr, cfg)
+	if err != nil {
+		return nil, err
+	}
+	if err := cn.Handshake(); err != nil {
+		return nil, err
+	}
+	if cfg.InsecureSkipVerify {
+		return cn, nil
+	}
+	if err := cn.VerifyHostname(cfg.ServerName); err != nil {
+		return nil, err
+	}
+	return cn, nil
+}
diff --git a/http2/transport.go b/http2/transport.go
index 5ae89cf..f89369e 100644
--- a/http2/transport.go
+++ b/http2/transport.go
@@ -595,14 +595,10 @@
 		return t.DialTLS
 	}
 	return func(network, addr string, cfg *tls.Config) (net.Conn, error) {
-		dialer := &tls.Dialer{
-			Config: cfg,
-		}
-		cn, err := dialer.DialContext(ctx, network, addr)
+		tlsCn, err := t.dialTLSWithContext(ctx, network, addr, cfg)
 		if err != nil {
 			return nil, err
 		}
-		tlsCn := cn.(*tls.Conn) // DialContext comment promises this will always succeed
 		state := tlsCn.ConnectionState()
 		if p := state.NegotiatedProtocol; p != NextProtoTLS {
 			return nil, fmt.Errorf("http2: unexpected ALPN protocol %q; want %q", p, NextProtoTLS)
@@ -610,7 +606,7 @@
 		if !state.NegotiatedProtocolIsMutual {
 			return nil, errors.New("http2: could not negotiate protocol mutually")
 		}
-		return cn, nil
+		return tlsCn, nil
 	}
 }