diff --git a/openpgp/packet/public_key.go b/openpgp/packet/public_key.go
index f8da781bb..6716febbe 100644
--- a/openpgp/packet/public_key.go
+++ b/openpgp/packet/public_key.go
@@ -908,9 +908,9 @@ func (pk *PublicKey) VerifyKeySignature(signed *PublicKey, sig *Signature) error
 		return err
 	}
 
-	if sig.FlagSign {
-		// Signing subkeys must be cross-signed. See
-		// https://www.gnupg.org/faq/subkey-cross-certify.html.
+	if sig.FlagSign || sig.FlagCertify || (sig.FlagAuthenticate && sig.Version == 6) {
+		// Subkeys that can issue signatures must be cross-signed. See
+		// https://www.rfc-editor.org/rfc/rfc9580.html#section-10.1.5-8.
 		if sig.EmbeddedSignature == nil {
 			return errors.StructuralError("signing subkey is missing cross-signature")
 		}
diff --git a/openpgp/v2/subkeys.go b/openpgp/v2/subkeys.go
index 3e9fc1890..e61d17fd3 100644
--- a/openpgp/v2/subkeys.go
+++ b/openpgp/v2/subkeys.go
@@ -181,25 +181,29 @@ func (s *Subkey) Revoke(reason packet.ReasonForRevocation, reasonText string, co
 // Returns a StructuralError if no valid self-signature is found.
 func (s *Subkey) LatestValidBindingSignature(date time.Time, config *packet.Config) (selectedSig *packet.Signature, err error) {
 	for sigIdx := len(s.Bindings) - 1; sigIdx >= 0; sigIdx-- {
-		sig := s.Bindings[sigIdx]
-		if (date.IsZero() || date.Unix() >= sig.Packet.CreationTime.Unix()) &&
-			(selectedSig == nil || selectedSig.CreationTime.Unix() < sig.Packet.CreationTime.Unix()) {
-			if sig.Valid == nil {
-				err := s.Primary.PrimaryKey.VerifyKeySignature(s.PublicKey, sig.Packet)
+		binding := s.Bindings[sigIdx]
+		sig := binding.Packet
+		if (date.IsZero() || date.Unix() >= sig.CreationTime.Unix()) &&
+			(selectedSig == nil || selectedSig.CreationTime.Unix() < sig.CreationTime.Unix()) {
+			if binding.Valid == nil {
+				err := s.Primary.PrimaryKey.VerifyKeySignature(s.PublicKey, sig)
 				if err == nil {
-					err = checkSignatureDetails(s.Primary.PrimaryKey, sig.Packet, date, config)
+					err = checkSignatureDetails(s.Primary.PrimaryKey, sig, date, config)
+				}
+				if err == nil && (sig.FlagSign || sig.FlagCertify || (sig.FlagAuthenticate && sig.Version == 6)) {
+					err = checkSignatureDetails(s.PublicKey, sig.EmbeddedSignature, date, config)
 				}
 				valid := err == nil
-				sig.Valid = &valid
+				binding.Valid = &valid
 			}
 			mainSigExpired := !date.IsZero() &&
-				sig.Packet.SigExpired(date)
+				sig.SigExpired(date)
 			embeddedSigExpired := !date.IsZero() &&
-				sig.Packet.FlagSign &&
-				sig.Packet.EmbeddedSignature != nil &&
-				sig.Packet.EmbeddedSignature.SigExpired(date)
-			if *sig.Valid && !mainSigExpired && !embeddedSigExpired {
-				selectedSig = sig.Packet
+				sig.FlagSign &&
+				sig.EmbeddedSignature != nil &&
+				sig.EmbeddedSignature.SigExpired(date)
+			if *binding.Valid && !mainSigExpired && !embeddedSigExpired {
+				selectedSig = sig
 			}
 		}
 	}