diff --git a/common.go b/common.go
index 9ea149a..c3ed291 100644
--- a/common.go
+++ b/common.go
@@ -155,11 +155,12 @@ const (
 	X25519MLKEM768     CurveID = 4588
 	SecP256r1MLKEM768  CurveID = 4587
 	SecP384r1MLKEM1024 CurveID = 4589
+	MLKEM1024          CurveID = 514
 )
 
 func isTLS13OnlyKeyExchange(curve CurveID) bool {
 	switch curve {
-	case X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024:
+	case X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024, MLKEM1024:
 		return true
 	default:
 		return false
@@ -168,7 +169,7 @@ func isTLS13OnlyKeyExchange(curve CurveID) bool {
 
 func isPQKeyExchange(curve CurveID) bool {
 	switch curve {
-	case X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024:
+	case X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024, MLKEM1024:
 		return true
 	default:
 		return false
diff --git a/common_string.go b/common_string.go
index bab3b84..09ce16c 100644
--- a/common_string.go
+++ b/common_string.go
@@ -82,17 +82,19 @@ func _() {
 	_ = x[X25519MLKEM768-4588]
 	_ = x[SecP256r1MLKEM768-4587]
 	_ = x[SecP384r1MLKEM1024-4589]
+	_ = x[MLKEM1024-514]
 }
 
 const (
 	_CurveID_name_0 = "CurveP256CurveP384CurveP521"
 	_CurveID_name_1 = "X25519"
-	_CurveID_name_2 = "SecP256r1MLKEM768X25519MLKEM768SecP384r1MLKEM1024"
+	_CurveID_name_2 = "MLKEM1024"
+	_CurveID_name_3 = "SecP256r1MLKEM768X25519MLKEM768SecP384r1MLKEM1024"
 )
 
 var (
 	_CurveID_index_0 = [...]uint8{0, 9, 18, 27}
-	_CurveID_index_2 = [...]uint8{0, 17, 31, 49}
+	_CurveID_index_3 = [...]uint8{0, 17, 31, 49}
 )
 
 func (i CurveID) String() string {
@@ -102,9 +104,11 @@ func (i CurveID) String() string {
 		return _CurveID_name_0[_CurveID_index_0[i]:_CurveID_index_0[i+1]]
 	case i == 29:
 		return _CurveID_name_1
+	case i == 514:
+		return _CurveID_name_2
 	case 4587 <= i && i <= 4589:
 		i -= 4587
-		return _CurveID_name_2[_CurveID_index_2[i]:_CurveID_index_2[i+1]]
+		return _CurveID_name_3[_CurveID_index_3[i]:_CurveID_index_3[i+1]]
 	default:
 		return "CurveID(" + strconv.FormatInt(int64(i), 10) + ")"
 	}
diff --git a/defaults.go b/defaults.go
index 17ab1d6..ee8f81b 100644
--- a/defaults.go
+++ b/defaults.go
@@ -37,7 +37,7 @@ func defaultCurveEnabled(c CurveID) bool {
 // include every supported key exchange.
 func curvePreferenceOrder() []CurveID {
 	return []CurveID{
-		X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024,
+		X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024, MLKEM1024,
 		X25519, CurveP256, CurveP384, CurveP521,
 	}
 }
diff --git a/defaults_fips140.go b/defaults_fips140.go
index 63bebd0..901e81d 100644
--- a/defaults_fips140.go
+++ b/defaults_fips140.go
@@ -35,6 +35,7 @@ var (
 		X25519MLKEM768,
 		SecP256r1MLKEM768,
 		SecP384r1MLKEM1024,
+		MLKEM1024,
 		CurveP256,
 		CurveP384,
 		CurveP521,
diff --git a/handshake_client.go b/handshake_client.go
index 94cd56a..0f47b51 100644
--- a/handshake_client.go
+++ b/handshake_client.go
@@ -140,7 +140,7 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, *keySharePrivateKeys, *echCli
 		}
 
 		if len(hello.supportedCurves) == 0 {
-			return nil, nil, nil, errors.New("tls: no supported elliptic curves for ECDHE")
+			return nil, nil, nil, errors.New("tls: no supported key exchange methods (CurveIDs)")
 		}
 		// Since the order is fixed, the first one is always the one to send a
 		// key share for. All the PQ hybrids sort first, and produce a fallback
diff --git a/handshake_client_tls13.go b/handshake_client_tls13.go
index e6db8e9..c15490b 100644
--- a/handshake_client_tls13.go
+++ b/handshake_client_tls13.go
@@ -54,7 +54,8 @@ func (hs *clientHandshakeStateTLS13) handshake() error {
 	}
 
 	// Consistency check on the presence of a keyShare and its parameters.
-	if hs.keyShareKeys == nil || hs.keyShareKeys.ecdhe == nil || len(hs.hello.keyShares) == 0 {
+	if hs.keyShareKeys == nil || (hs.keyShareKeys.ecdhe == nil && hs.keyShareKeys.mlkem == nil) ||
+		len(hs.hello.keyShares) == 0 {
 		return c.sendAlert(alertInternalError)
 	}
 
diff --git a/key_schedule.go b/key_schedule.go
index b798bdd..c2d09ca 100644
--- a/key_schedule.go
+++ b/key_schedule.go
@@ -108,11 +108,40 @@ func keyExchangeForCurveID(id CurveID) (keyExchange, error) {
 		return &hybridKeyExchange{id, ecdhKeyExchange{CurveP384, ecdh.P384()},
 			97, mlkem.EncapsulationKeySize1024, mlkem.CiphertextSize1024,
 			mlkemGenerateKey1024, mlkemNewPublicKey1024}, nil
+	case MLKEM1024:
+		return &mlkem1024KeyExchange{}, nil
 	default:
 		return nil, errors.New("tls: unsupported key exchange")
 	}
 }
 
+type mlkem1024KeyExchange struct{}
+
+func (ke *mlkem1024KeyExchange) keyShares(_ io.Reader) (*keySharePrivateKeys, []keyShare, error) {
+	priv, err := mlkem.GenerateKey1024()
+	if err != nil {
+		return nil, nil, err
+	}
+	return &keySharePrivateKeys{mlkem: priv}, []keyShare{{MLKEM1024, priv.EncapsulationKey().Bytes()}}, nil
+}
+
+func (ke *mlkem1024KeyExchange) serverSharedSecret(_ io.Reader, clientKeyShare []byte) ([]byte, keyShare, error) {
+	peerKey, err := mlkem.NewEncapsulationKey1024(clientKeyShare)
+	if err != nil {
+		return nil, keyShare{}, err
+	}
+	sharedKey, keyShareData := peerKey.Encapsulate()
+	return sharedKey, keyShare{MLKEM1024, keyShareData}, nil
+}
+
+func (ke *mlkem1024KeyExchange) clientSharedSecret(priv *keySharePrivateKeys, serverKeyShare []byte) ([]byte, error) {
+	sharedKey, err := priv.mlkem.Decapsulate(serverKeyShare)
+	if err != nil {
+		return nil, err
+	}
+	return sharedKey, nil
+}
+
 type ecdhKeyExchange struct {
 	id    CurveID
 	curve ecdh.Curve