diff --git a/bin/millau/runtime/src/lib.rs b/bin/millau/runtime/src/lib.rs
index fbc3f8e374..40be3223ed 100644
--- a/bin/millau/runtime/src/lib.rs
+++ b/bin/millau/runtime/src/lib.rs
@@ -568,7 +568,7 @@ construct_runtime!(
 	}
 );
 
-pallet_bridge_grandpa::declare_check_bridged_block_number_ext! {
+pallet_bridge_grandpa::declare_bridge_reject_obsolete_grandpa_header! {
 	Runtime,
 	Call::BridgeRialtoGrandpa => RialtoGrandpaInstance,
 	Call::BridgeWestendGrandpa => WestendGrandpaInstance
@@ -594,7 +594,7 @@ pub type SignedExtra = (
 	frame_system::CheckNonce<Runtime>,
 	frame_system::CheckWeight<Runtime>,
 	pallet_transaction_payment::ChargeTransactionPayment<Runtime>,
-	CheckBridgedBlockNumber,
+	BridgeRejectObsoleteGrandpaHeader,
 );
 /// The payload being signed in transactions.
 pub type SignedPayload = generic::SignedPayload<Call, SignedExtra>;
diff --git a/modules/grandpa/src/extension.rs b/modules/grandpa/src/extension.rs
index 4a7d19acf2..43ad622105 100644
--- a/modules/grandpa/src/extension.rs
+++ b/modules/grandpa/src/extension.rs
@@ -14,27 +14,27 @@
 // You should have received a copy of the GNU General Public License
 // along with Parity Bridges Common.  If not, see <http://www.gnu.org/licenses/>.
 
-/// Declares a runtime-specific `CheckBridgedBlockNumber` signed extension.
+/// Declares a runtime-specific `BridgeRejectObsoleteGrandpaHeader` signed extension.
 ///
 /// ## Example
 ///
 /// ```nocompile
-/// pallet_bridge_grandpa::declare_check_bridged_block_number_ext!{
+/// pallet_bridge_grandpa::declare_bridge_reject_obsolete_grandpa_header!{
 ///     Runtime,
 ///     Call::BridgeRialtoGrandpa => RialtoGrandpaInstance,
 ///     Call::BridgeWestendGrandpa => WestendGrandpaInstance,
 /// }
 /// ```
 #[macro_export]
-macro_rules! declare_check_bridged_block_number_ext {
+macro_rules! declare_bridge_reject_obsolete_grandpa_header {
 	($runtime:ident, $($call:path => $instance:ty),*) => {
 		/// Transaction-with-obsolete-bridged-header check that will reject transaction if
 		/// it submits obsolete bridged header.
 		#[derive(Clone, codec::Decode, codec::Encode, Eq, PartialEq, frame_support::RuntimeDebug, scale_info::TypeInfo)]
-		pub struct CheckBridgedBlockNumber;
+		pub struct BridgeRejectObsoleteGrandpaHeader;
 
-		impl sp_runtime::traits::SignedExtension for CheckBridgedBlockNumber {
-			const IDENTIFIER: &'static str = "CheckBridgedBlockNumber";
+		impl sp_runtime::traits::SignedExtension for BridgeRejectObsoleteGrandpaHeader {
+			const IDENTIFIER: &'static str = "BridgeRejectObsoleteGrandpaHeader";
 			type AccountId = <$runtime as frame_system::Config>::AccountId;
 			type Call = <$runtime as frame_system::Config>::Call;
 			type AdditionalSigned = ();
@@ -114,13 +114,13 @@ mod tests {
 	use frame_support::weights::{DispatchClass, DispatchInfo, Pays};
 	use sp_runtime::traits::SignedExtension;
 
-	declare_check_bridged_block_number_ext! {
+	declare_bridge_reject_obsolete_grandpa_header! {
 		TestRuntime,
 		Call::Grandpa => ()
 	}
 
 	fn validate_block_submit(num: TestNumber) -> bool {
-		CheckBridgedBlockNumber
+		BridgeRejectObsoleteGrandpaHeader
 			.validate(
 				&42,
 				&Call::Grandpa(crate::Call::<TestRuntime, ()>::submit_finality_proof {
@@ -140,7 +140,7 @@ mod tests {
 	}
 
 	#[test]
-	fn check_bridged_block_number_rejects_obsolete_header() {
+	fn extension_rejects_obsolete_header() {
 		run_test(|| {
 			// when current best finalized is #10 and we're trying to import header#5 => tx is
 			// rejected
@@ -150,7 +150,7 @@ mod tests {
 	}
 
 	#[test]
-	fn check_bridged_block_number_rejects_same_header() {
+	fn extension_rejects_same_header() {
 		run_test(|| {
 			// when current best finalized is #10 and we're trying to import header#10 => tx is
 			// rejected
@@ -160,7 +160,7 @@ mod tests {
 	}
 
 	#[test]
-	fn check_bridged_block_number_accepts_new_header() {
+	fn extension_accepts_new_header() {
 		run_test(|| {
 			// when current best finalized is #10 and we're trying to import header#15 => tx is
 			// accepted
diff --git a/relays/client-millau/src/lib.rs b/relays/client-millau/src/lib.rs
index 1fa4708368..2779fb0fd3 100644
--- a/relays/client-millau/src/lib.rs
+++ b/relays/client-millau/src/lib.rs
@@ -115,7 +115,7 @@ impl TransactionSignScheme for Millau {
 				frame_system::CheckNonce::<millau_runtime::Runtime>::from(param.unsigned.nonce),
 				frame_system::CheckWeight::<millau_runtime::Runtime>::new(),
 				pallet_transaction_payment::ChargeTransactionPayment::<millau_runtime::Runtime>::from(param.unsigned.tip),
-				millau_runtime::CheckBridgedBlockNumber, // TODO
+				millau_runtime::BridgeRejectObsoleteGrandpaHeader,
 			),
 			(
 				(),