diff --git a/handshake_client_tls13.go b/handshake_client_tls13.go
index 53b5eba..99fd6ea 100644
--- a/handshake_client_tls13.go
+++ b/handshake_client_tls13.go
@@ -629,6 +629,15 @@ func (hs *clientHandshakeStateTLS13) establishHandshakeKeys() error {
 		}
 		ecdhePeerData = hs.serverHello.serverShare.data[mlkem.CiphertextSize768:]
 	}
+	// [uTLS] SECTION BEGIN
+	if hs.serverHello.serverShare.group == X25519Kyber768Draft00 {
+		if len(ecdhePeerData) != x25519PublicKeySize+mlkem.CiphertextSize768 {
+			c.sendAlert(alertIllegalParameter)
+			return errors.New("tls: invalid server X25519Kyber768Draft00 key share")
+		}
+		ecdhePeerData = hs.serverHello.serverShare.data[:x25519PublicKeySize]
+	}
+	// [uTLS] SECTION END
 	peerKey, err := hs.keyShareKeys.ecdhe.Curve().NewPublicKey(ecdhePeerData)
 	if err != nil {
 		c.sendAlert(alertIllegalParameter)
@@ -651,6 +660,20 @@ func (hs *clientHandshakeStateTLS13) establishHandshakeKeys() error {
 		}
 		sharedKey = append(mlkemShared, sharedKey...)
 	}
+	// [uTLS] SECTION BEGIN
+	if hs.serverHello.serverShare.group == X25519Kyber768Draft00 {
+		if hs.keyShareKeys.mlkem == nil {
+			return c.sendAlert(alertInternalError)
+		}
+		ciphertext := hs.serverHello.serverShare.data[x25519PublicKeySize:]
+		kyberShared, err := kyberDecapsulate(hs.keyShareKeys.mlkem, ciphertext)
+		if err != nil {
+			c.sendAlert(alertIllegalParameter)
+			return errors.New("tls: invalid X25519Kyber768Draft00 server key share")
+		}
+		sharedKey = append(sharedKey, kyberShared...)
+	}
+	// [uTLS] SECTION END
 	c.curveID = hs.serverHello.serverShare.group
 
 	earlySecret := hs.earlySecret
diff --git a/u_common.go b/u_common.go
index 860b925..d43849b 100644
--- a/u_common.go
+++ b/u_common.go
@@ -88,7 +88,7 @@ const (
 )
 
 const (
-	// X25519Kyber768Draft00 CurveID = x25519Kyber768Draft00
+	X25519Kyber768Draft00 CurveID = 0x6399
 
 	FakeCurveX25519Kyber512Draft00    CurveID = 0xfe30
 	FakeCurveX25519Kyber768Draft00Old CurveID = 0xfe31
diff --git a/u_key_schedule.go b/u_key_schedule.go
new file mode 100644
index 0000000..f52839d
--- /dev/null
+++ b/u_key_schedule.go
@@ -0,0 +1,30 @@
+package tls
+
+import (
+	"crypto/mlkem"
+
+	"golang.org/x/crypto/sha3"
+)
+
+// kyberDecapsulate implements decapsulation according to Kyber Round 3.
+func kyberDecapsulate(dk *mlkem.DecapsulationKey768, c []byte) ([]byte, error) {
+	K, err := dk.Decapsulate(c)
+	if err != nil {
+		return nil, err
+	}
+	return kyberSharedSecret(c, K), nil
+}
+
+func kyberSharedSecret(c, K []byte) []byte {
+	// Package mlkem implements ML-KEM, which compared to Kyber removed a
+	// final hashing step. Compute SHAKE-256(K || SHA3-256(c), 32) to match Kyber.
+	// See https://words.filippo.io/mlkem768/#bonus-track-using-a-ml-kem-implementation-as-kyber-v3.
+	h := sha3.NewShake256()
+	h.Write(K)
+	ch := sha3.New256()
+	ch.Write(c)
+	h.Write(ch.Sum(nil))
+	out := make([]byte, 32)
+	h.Read(out)
+	return out
+}
diff --git a/u_parrots.go b/u_parrots.go
index 78b7f6a..69c2636 100644
--- a/u_parrots.go
+++ b/u_parrots.go
@@ -618,7 +618,7 @@ func utlsIdToSpec(id ClientHelloID) (ClientHelloSpec, error) {
 				&RenegotiationInfoExtension{Renegotiation: RenegotiateOnceAsClient},
 				&SupportedCurvesExtension{[]CurveID{
 					GREASE_PLACEHOLDER,
-					X25519MLKEM768,
+					X25519Kyber768Draft00,
 					X25519,
 					CurveP256,
 					CurveP384,
@@ -642,7 +642,7 @@ func utlsIdToSpec(id ClientHelloID) (ClientHelloSpec, error) {
 				&SCTExtension{},
 				&KeyShareExtension{[]KeyShare{
 					{Group: CurveID(GREASE_PLACEHOLDER), Data: []byte{0}},
-					{Group: X25519MLKEM768},
+					{Group: X25519Kyber768Draft00},
 					{Group: X25519},
 				}},
 				&PSKKeyExchangeModesExtension{[]uint8{
@@ -764,7 +764,7 @@ func utlsIdToSpec(id ClientHelloID) (ClientHelloSpec, error) {
 				&RenegotiationInfoExtension{Renegotiation: RenegotiateOnceAsClient},
 				&SupportedCurvesExtension{[]CurveID{
 					GREASE_PLACEHOLDER,
-					X25519MLKEM768,
+					X25519Kyber768Draft00,
 					X25519,
 					CurveP256,
 					CurveP384,
@@ -788,7 +788,7 @@ func utlsIdToSpec(id ClientHelloID) (ClientHelloSpec, error) {
 				&SCTExtension{},
 				&KeyShareExtension{[]KeyShare{
 					{Group: CurveID(GREASE_PLACEHOLDER), Data: []byte{0}},
-					{Group: X25519MLKEM768},
+					{Group: X25519Kyber768Draft00},
 					{Group: X25519},
 				}},
 				&PSKKeyExchangeModesExtension{[]uint8{
@@ -2495,7 +2495,7 @@ func utlsIdToSpec(id ClientHelloID) (ClientHelloSpec, error) {
 				&RenegotiationInfoExtension{Renegotiation: RenegotiateOnceAsClient},
 				&SupportedCurvesExtension{[]CurveID{
 					GREASE_PLACEHOLDER,
-					X25519MLKEM768,
+					X25519Kyber768Draft00,
 					X25519,
 					CurveP256,
 					CurveP384,
@@ -2519,7 +2519,7 @@ func utlsIdToSpec(id ClientHelloID) (ClientHelloSpec, error) {
 				&SCTExtension{},
 				&KeyShareExtension{[]KeyShare{
 					{Group: CurveID(GREASE_PLACEHOLDER), Data: []byte{0}},
-					{Group: X25519MLKEM768},
+					{Group: X25519Kyber768Draft00},
 					{Group: X25519},
 				}},
 				&PSKKeyExchangeModesExtension{[]uint8{
@@ -2736,7 +2736,7 @@ func (uconn *UConn) ApplyPreset(p *ClientHelloSpec) error {
 					continue
 				}
 
-				if curveID == X25519MLKEM768 {
+				if curveID == X25519MLKEM768 || curveID == X25519Kyber768Draft00 {
 					ecdheKey, err := generateECDHEKey(uconn.config.rand(), X25519)
 					if err != nil {
 						return err
@@ -2756,7 +2756,11 @@ func (uconn *UConn) ApplyPreset(p *ClientHelloSpec) error {
 					// }
 					// uconn.HandshakeState.State13.KeySharesParams.AddKemKeypair(curveID, circlKyberKey, circlKyberKey.Public())
 
-					ext.KeyShares[i].Data = append(mlkemKey.EncapsulationKey().Bytes(), ecdheKey.PublicKey().Bytes()...)
+					if curveID == X25519Kyber768Draft00 {
+						ext.KeyShares[i].Data = append(ecdheKey.PublicKey().Bytes(), mlkemKey.EncapsulationKey().Bytes()...)
+					} else {
+						ext.KeyShares[i].Data = append(mlkemKey.EncapsulationKey().Bytes(), ecdheKey.PublicKey().Bytes()...)
+					}
 					if !preferredCurveIsSet {
 						// only do this once for the first non-grease curve
 						uconn.HandshakeState.State13.KeyShareKeys.mlkem = mlkemKey