diff --git a/common.go b/common.go
index 992a163..6ae3fca 100644
--- a/common.go
+++ b/common.go
@@ -785,11 +785,16 @@ func (c *Config) curvePreferences() []CurveID {
 }
 
 // mutualVersion returns the protocol version to use given the advertised
-// version of the peer.
+// version of the peer using the legacy non-extension methods.
 func (c *Config) mutualVersion(vers uint16) (uint16, bool) {
 	minVersion := c.minVersion()
 	maxVersion := c.maxVersion()
 
+	// Version 1.3 and higher are not negotiated via this mechanism.
+	if maxVersion > VersionTLS12 {
+		maxVersion = VersionTLS12
+	}
+
 	if vers < minVersion {
 		return 0, false
 	}
@@ -799,6 +804,33 @@ func (c *Config) mutualVersion(vers uint16) (uint16, bool) {
 	return vers, true
 }
 
+// pickVersion returns the protocol version to use given the advertised
+// versions of the peer using the Supported Versions extension.
+func (c *Config) pickVersion(supportedVersions []uint16) (uint16, bool) {
+	minVersion := c.minVersion()
+	maxVersion := c.maxVersion()
+	if c == nil || c.MaxVersion == 0 {
+		maxVersion = VersionTLS13 // override the default if pickVersion is used
+	}
+
+	tls13Enabled := maxVersion >= VersionTLS13
+	if maxVersion > VersionTLS12 {
+		maxVersion = VersionTLS12
+	}
+
+	var vers uint16
+	for _, v := range supportedVersions {
+		if v >= minVersion && v <= maxVersion ||
+			(tls13Enabled && v == VersionTLS13Draft18) {
+			if v > vers {
+				vers = v
+			}
+		}
+	}
+
+	return vers, vers != 0
+}
+
 // getCertificate returns the best certificate for the given ClientHelloInfo,
 // defaulting to the first element of c.Certificates.
 func (c *Config) getCertificate(clientHello *ClientHelloInfo) (*Certificate, error) {
diff --git a/handshake_server.go b/handshake_server.go
index c6427b2..7a9a428 100644
--- a/handshake_server.go
+++ b/handshake_server.go
@@ -171,14 +171,8 @@ func (hs *serverHandshakeState) readClientHello() (isResume bool, err error) {
 	}
 
 	if hs.clientHello.supportedVersions != nil {
-		for _, v := range hs.clientHello.supportedVersions {
-			if (v >= c.config.minVersion() && v <= c.config.maxVersion()) ||
-				v == VersionTLS13Draft18 {
-				c.vers = v
-				break
-			}
-		}
-		if c.vers == 0 {
+		c.vers, ok = c.config.pickVersion(hs.clientHello.supportedVersions)
+		if !ok {
 			c.sendAlert(alertProtocolVersion)
 			return false, fmt.Errorf("tls: none of the client versions (%x) are supported", hs.clientHello.supportedVersions)
 		}