diff --git a/transport/tls/stream_dialer.go b/transport/tls/stream_dialer.go
index 2a72d70a..23884bbd 100644
--- a/transport/tls/stream_dialer.go
+++ b/transport/tls/stream_dialer.go
@@ -17,6 +17,7 @@ package tls
 import (
 	"context"
 	"crypto/tls"
+	"crypto/x509"
 	"errors"
 	"fmt"
 	"net"
@@ -71,17 +72,40 @@ func (d *StreamDialer) Dial(ctx context.Context, remoteAddr string) (transport.S
 
 // clientConfig encodes the parameters for a TLS client connection.
 type clientConfig struct {
-	ServerName   string
-	NextProtos   []string
-	SessionCache tls.ClientSessionCache
+	ServerName      string
+	CertificateName string
+	NextProtos      []string
+	SessionCache    tls.ClientSessionCache
 }
 
 // ToStdConfig creates a [tls.Config] based on the configured parameters.
 func (cfg *clientConfig) ToStdConfig() *tls.Config {
+	certificateName := cfg.CertificateName
+	if certificateName == "" {
+		certificateName = cfg.ServerName
+	}
 	return &tls.Config{
 		ServerName:         cfg.ServerName,
 		NextProtos:         cfg.NextProtos,
 		ClientSessionCache: cfg.SessionCache,
+		// Set InsecureSkipVerify to skip the default validation we are
+		// replacing. This will not disable VerifyConnection.
+		InsecureSkipVerify: true,
+		VerifyConnection: func(cs tls.ConnectionState) error {
+			// This replicates the logic in the standard library verification:
+			// https://cs.opensource.google/go/go/+/master:src/crypto/tls/handshake_client.go;l=982;drc=b5f87b5407916c4049a3158cc944cebfd7a883a9
+			// And the documentation example:
+			// https://pkg.go.dev/crypto/tls#example-Config-VerifyConnection
+			opts := x509.VerifyOptions{
+				DNSName:       certificateName,
+				Intermediates: x509.NewCertPool(),
+			}
+			for _, cert := range cs.PeerCertificates[1:] {
+				opts.Intermediates.AddCert(cert)
+			}
+			_, err := cs.PeerCertificates[0].Verify(opts)
+			return err
+		},
 	}
 }
 
@@ -131,3 +155,11 @@ func WithSessionCache(sessionCache tls.ClientSessionCache) ClientOption {
 		config.SessionCache = sessionCache
 	}
 }
+
+// WithCertificateName sets the hostname to be used for the certificate validation.
+// If absent, defaults to SNI.
+func WithCertificateName(hostname string) ClientOption {
+	return func(_ string, _ int, config *clientConfig) {
+		config.CertificateName = hostname
+	}
+}
diff --git a/transport/tls/stream_dialer_test.go b/transport/tls/stream_dialer_test.go
index cbe23854..5fb4f70a 100644
--- a/transport/tls/stream_dialer_test.go
+++ b/transport/tls/stream_dialer_test.go
@@ -23,7 +23,7 @@ import (
 )
 
 func TestDomainFronting(t *testing.T) {
-	sd, err := NewStreamDialer(&transport.TCPStreamDialer{}, WithSNI("www.youtube.com"))
+	sd, err := NewStreamDialer(&transport.TCPStreamDialer{}, WithSNI("decoy.android.com"), WithCertificateName("www.youtube.com"))
 	require.NoError(t, err)
 	conn, err := sd.Dial(context.Background(), "www.google.com:443")
 	require.NoError(t, err)