diff --git a/common.go b/common.go
index 67c6994..dc4adae 100644
--- a/common.go
+++ b/common.go
@@ -1310,25 +1310,32 @@ func supportedVersionsFromMax(maxVersion uint16) []uint16 {
 }
 
 func (c *Config) curvePreferences(version uint16) []CurveID {
-	curvePreferences := defaultCurvePreferences()
-	if fips140tls.Required() {
-		curvePreferences = slices.DeleteFunc(curvePreferences, func(x CurveID) bool {
-			return !slices.Contains(allowedCurvePreferencesFIPS, x)
-		})
-	}
-	if c != nil && len(c.CurvePreferences) != 0 {
-		curvePreferences = slices.DeleteFunc(curvePreferences, func(x CurveID) bool {
-			return !slices.Contains(c.CurvePreferences, x)
-		})
-	}
-	if version < VersionTLS13 {
-		curvePreferences = slices.DeleteFunc(curvePreferences, isTLS13OnlyKeyExchange)
-	}
-	return curvePreferences
+	return slices.DeleteFunc(curvePreferenceOrder(), func(x CurveID) bool {
+		return !c.supportsCurve(version, x)
+	})
 }
 
-func (c *Config) supportsCurve(version uint16, curve CurveID) bool {
-	return slices.Contains(c.curvePreferences(version), curve)
+func (c *Config) supportsCurve(version uint16, x CurveID) bool {
+	if c != nil && len(c.CurvePreferences) != 0 {
+		if !slices.Contains(c.CurvePreferences, x) {
+			return false
+		}
+		// Ignore unimplemented entries in c.CurvePreferences.
+		if !slices.Contains(curvePreferenceOrder(), x) {
+			return false
+		}
+	} else {
+		if !defaultCurveEnabled(x) {
+			return false
+		}
+	}
+	if fips140tls.Required() && !slices.Contains(allowedCurvePreferencesFIPS, x) {
+		return false
+	}
+	if version < VersionTLS13 && isTLS13OnlyKeyExchange(x) {
+		return false
+	}
+	return true
 }
 
 // mutualVersion returns the protocol version to use given the advertised
diff --git a/defaults.go b/defaults.go
index 5c03801..17ab1d6 100644
--- a/defaults.go
+++ b/defaults.go
@@ -12,24 +12,33 @@ import (
 // Defaults are collected in this file to allow distributions to more easily patch
 // them to apply local policies.
 
+// tlsmlkem=0 restores the pre-Go 1.24 default key exchanges.
 //var tlsmlkem = godebug.New("tlsmlkem")
+
+// tlssecpmlkem=0 restores the pre-Go 1.26 default key exchanges.
 //var tlssecpmlkem = godebug.New("tlssecpmlkem")
 
-// defaultCurvePreferences is the default set of supported key exchanges, as
-// well as the preference order.
-func defaultCurvePreferences() []CurveID {
-	switch {
-	// // tlsmlkem=0 restores the pre-Go 1.24 default.
-	// case tlsmlkem.Value() == "0":
-	// 	return []CurveID{X25519, CurveP256, CurveP384, CurveP521}
-	// // tlssecpmlkem=0 restores the pre-Go 1.26 default.
-	// case tlssecpmlkem.Value() == "0":
-	// 	return []CurveID{X25519MLKEM768, X25519, CurveP256, CurveP384, CurveP521}
+// defaultCurveEnabled returns whether the key exchange c is enabled by default.
+func defaultCurveEnabled(c CurveID) bool {
+	switch c {
+	case X25519, CurveP256, CurveP384, CurveP521:
+		return true
+	case X25519MLKEM768:
+		return true//tlsmlkem.Value() != "0"
+	case SecP256r1MLKEM768, SecP384r1MLKEM1024:
+		return true//tlsmlkem.Value() != "0" && tlssecpmlkem.Value() != "0"
+
 	default:
-		return []CurveID{
-			X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024,
-			X25519, CurveP256, CurveP384, CurveP521,
-		}
+		return false
+	}
+}
+
+// curvePreferenceOrder is the fixed preference order of key exchanges. It must
+// include every supported key exchange.
+func curvePreferenceOrder() []CurveID {
+	return []CurveID{
+		X25519MLKEM768, SecP256r1MLKEM768, SecP384r1MLKEM1024,
+		X25519, CurveP256, CurveP384, CurveP521,
 	}
 }
 
diff --git a/handshake_client.go b/handshake_client.go
index 22aed23..94cd56a 100644
--- a/handshake_client.go
+++ b/handshake_client.go
@@ -148,7 +148,7 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, *keySharePrivateKeys, *echCli
 		curveID := hello.supportedCurves[0]
 		ke, err := keyExchangeForCurveID(curveID)
 		if err != nil {
-			return nil, nil, nil, errors.New("tls: CurvePreferences includes unsupported curve")
+			return nil, nil, nil, errors.New("tls: internal error: supportsCurve accepted unimplemented curve")
 		}
 		keyShareKeys, hello.keyShares, err = ke.keyShares(config.rand())
 		if err != nil {
diff --git a/handshake_client_tls13.go b/handshake_client_tls13.go
index 0084dc7..e6db8e9 100644
--- a/handshake_client_tls13.go
+++ b/handshake_client_tls13.go
@@ -322,7 +322,7 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error {
 		ke, err := keyExchangeForCurveID(curveID)
 		if err != nil {
 			c.sendAlert(alertInternalError)
-			return errors.New("tls: CurvePreferences includes unsupported curve")
+			return errors.New("tls: internal error: supportsCurve accepted unimplemented curve")
 		}
 		hs.keyShareKeys, hello.keyShares, err = ke.keyShares(c.config.rand())
 		if err != nil {
diff --git a/handshake_server_tls13.go b/handshake_server_tls13.go
index 673843f..7ae0f6b 100644
--- a/handshake_server_tls13.go
+++ b/handshake_server_tls13.go
@@ -343,7 +343,7 @@ func (hs *serverHandshakeStateTLS13) processClientHello() error {
 	ke, err := keyExchangeForCurveID(selectedGroup)
 	if err != nil {
 		c.sendAlert(alertInternalError)
-		return errors.New("tls: CurvePreferences includes unsupported curve")
+		return errors.New("tls: internal error: supportsCurve accepted unimplemented curve")
 	}
 	hs.sharedKey, hs.hello.serverShare, err = ke.serverSharedSecret(c.config.rand(), clientKeyShare.data)
 	if err != nil {
diff --git a/key_agreement.go b/key_agreement.go
index 220df9a..099cf88 100644
--- a/key_agreement.go
+++ b/key_agreement.go
@@ -167,7 +167,7 @@ func (ka *ecdheKeyAgreement) generateServerKeyExchange(config *Config, cert *Cer
 		return nil, errors.New("tls: no supported elliptic curves offered")
 	}
 	if _, ok := curveForCurveID(ka.curveID); !ok {
-		return nil, errors.New("tls: CurvePreferences includes unsupported curve")
+		return nil, errors.New("tls: internal error: supportsCurve accepted unimplemented curve")
 	}
 
 	key, err := generateECDHEKey(config.rand(), ka.curveID)