diff --git a/bridges/bin/millau/runtime/Cargo.toml b/bridges/bin/millau/runtime/Cargo.toml
index 13195b9519..4fe2f72a96 100644
--- a/bridges/bin/millau/runtime/Cargo.toml
+++ b/bridges/bin/millau/runtime/Cargo.toml
@@ -10,12 +10,14 @@ license = "GPL-3.0-or-later WITH Classpath-exception-2.0"
 [dependencies]
 hex-literal = "0.3"
 codec = { package = "parity-scale-codec", version = "2.2.0", default-features = false, features = ["derive"] }
+libsecp256k1 = { version = "0.7", optional = true, default-features = false, features = ["hmac"] }
 scale-info = { version = "1.0", default-features = false, features = ["derive"] }
 serde = { version = "1.0", optional = true, features = ["derive"] }
 
 # Bridge dependencies
 
 bp-header-chain = { path = "../../../primitives/header-chain", default-features = false }
+bp-message-dispatch = { path = "../../../primitives/message-dispatch", default-features = false }
 bp-messages = { path = "../../../primitives/messages", default-features = false }
 bp-millau = { path = "../../../primitives/chain-millau", default-features = false }
 bp-rialto = { path = "../../../primitives/chain-rialto", default-features = false }
@@ -71,6 +73,7 @@ default = ["std"]
 std = [
 	"beefy-primitives/std",
 	"bp-header-chain/std",
+	"bp-message-dispatch/std",
 	"bp-messages/std",
 	"bp-millau/std",
 	"bp-rialto/std",
@@ -116,8 +119,12 @@ std = [
 	"sp-version/std",
 ]
 runtime-benchmarks = [
+	"bridge-runtime-common/runtime-benchmarks",
 	"frame-benchmarking",
 	"frame-support/runtime-benchmarks",
 	"frame-system/runtime-benchmarks",
+	"libsecp256k1",
+	"pallet-bridge-messages/runtime-benchmarks",
 	"pallet-bridge-token-swap/runtime-benchmarks",
+	"sp-runtime/runtime-benchmarks",
 ]
diff --git a/bridges/bin/millau/runtime/src/lib.rs b/bridges/bin/millau/runtime/src/lib.rs
index b4a80659ab..4d6ecd8ba3 100644
--- a/bridges/bin/millau/runtime/src/lib.rs
+++ b/bridges/bin/millau/runtime/src/lib.rs
@@ -374,12 +374,26 @@ parameter_types! {
 	// Note that once this is hit the pallet will essentially throttle incoming requests down to one
 	// call per block.
 	pub const MaxRequests: u32 = 50;
+}
 
-	// Number of headers to keep.
-	//
-	// Assuming the worst case of every header being finalized, we will keep headers for at least a
-	// week.
-	pub const HeadersToKeep: u32 = 7 * bp_millau::DAYS as u32;
+#[cfg(feature = "runtime-benchmarks")]
+parameter_types! {
+	/// Number of headers to keep in benchmarks.
+	///
+	/// In benchmarks we always populate with full number of `HeadersToKeep` to make sure that
+	/// pruning is taken into account.
+	///
+	/// Note: This is lower than regular value, to speed up benchmarking setup.
+	pub const HeadersToKeep: u32 = 1024;
+}
+
+#[cfg(not(feature = "runtime-benchmarks"))]
+parameter_types! {
+	/// Number of headers to keep.
+	///
+	/// Assuming the worst case of every header being finalized, we will keep headers at least for a
+	/// week.
+	pub const HeadersToKeep: u32 = 7 * bp_rialto::DAYS as u32;
 }
 
 pub type RialtoGrandpaInstance = ();
@@ -388,8 +402,7 @@ impl pallet_bridge_grandpa::Config for Runtime {
 	type MaxRequests = MaxRequests;
 	type HeadersToKeep = HeadersToKeep;
 
-	// TODO [#391]: Use weights generated for the Millau runtime instead of Rialto ones.
-	type WeightInfo = pallet_bridge_grandpa::weights::RialtoWeight<Runtime>;
+	type WeightInfo = pallet_bridge_grandpa::weights::MillauWeight<Runtime>;
 }
 
 pub type WestendGrandpaInstance = pallet_bridge_grandpa::Instance1;
@@ -398,8 +411,7 @@ impl pallet_bridge_grandpa::Config<WestendGrandpaInstance> for Runtime {
 	type MaxRequests = MaxRequests;
 	type HeadersToKeep = HeadersToKeep;
 
-	// TODO [#391]: Use weights generated for the Millau runtime instead of Rialto ones.
-	type WeightInfo = pallet_bridge_grandpa::weights::RialtoWeight<Runtime>;
+	type WeightInfo = pallet_bridge_grandpa::weights::MillauWeight<Runtime>;
 }
 
 impl pallet_shift_session_manager::Config for Runtime {}
@@ -422,8 +434,7 @@ pub type WithRialtoMessagesInstance = ();
 
 impl pallet_bridge_messages::Config<WithRialtoMessagesInstance> for Runtime {
 	type Event = Event;
-	// TODO: https://github.com/paritytech/parity-bridges-common/issues/390
-	type WeightInfo = pallet_bridge_messages::weights::RialtoWeight<Runtime>;
+	type WeightInfo = pallet_bridge_messages::weights::MillauWeight<Runtime>;
 	type Parameter = rialto_messages::MillauToRialtoMessagesParameter;
 	type MaxMessagesToPruneAtOnce = MaxMessagesToPruneAtOnce;
 	type MaxUnrewardedRelayerEntriesAtInboundLane = MaxUnrewardedRelayerEntriesAtInboundLane;
@@ -783,9 +794,13 @@ impl_runtime_apis! {
 			use frame_benchmarking::{list_benchmark, Benchmarking, BenchmarkList};
 			use frame_support::traits::StorageInfoTrait;
 
+			use pallet_bridge_messages::benchmarking::Pallet as MessagesBench;
+
 			let mut list = Vec::<BenchmarkList>::new();
 
 			list_benchmark!(list, extra, pallet_bridge_token_swap, BridgeRialtoTokenSwap);
+			list_benchmark!(list, extra, pallet_bridge_messages, MessagesBench::<Runtime, WithRialtoMessagesInstance>);
+			list_benchmark!(list, extra, pallet_bridge_grandpa, BridgeRialtoGrandpa);
 
 			let storage_info = AllPalletsWithSystem::storage_info();
 
@@ -813,6 +828,171 @@ impl_runtime_apis! {
 			let mut batches = Vec::<BenchmarkBatch>::new();
 			let params = (&config, &whitelist);
 
+			use bp_runtime::messages::DispatchFeePayment;
+			use bridge_runtime_common::messages;
+			use pallet_bridge_messages::benchmarking::{
+				Pallet as MessagesBench,
+				Config as MessagesConfig,
+				MessageDeliveryProofParams,
+				MessageParams,
+				MessageProofParams,
+				ProofSize as MessagesProofSize,
+			};
+			use rialto_messages::{ToRialtoMessagePayload, WithRialtoMessageBridge};
+
+			impl MessagesConfig<WithRialtoMessagesInstance> for Runtime {
+				fn maximal_message_size() -> u32 {
+					messages::source::maximal_message_size::<WithRialtoMessageBridge>()
+				}
+
+				fn bridged_relayer_id() -> Self::InboundRelayer {
+					Default::default()
+				}
+
+				fn account_balance(account: &Self::AccountId) -> Self::OutboundMessageFee {
+					pallet_balances::Pallet::<Runtime>::free_balance(account)
+				}
+
+				fn endow_account(account: &Self::AccountId) {
+					pallet_balances::Pallet::<Runtime>::make_free_balance_be(
+						account,
+						Balance::MAX / 100,
+					);
+				}
+
+				fn prepare_outbound_message(
+					params: MessageParams<Self::AccountId>,
+				) -> (rialto_messages::ToRialtoMessagePayload, Balance) {
+					let message_payload = vec![0; params.size as usize];
+					let dispatch_origin = bp_message_dispatch::CallOrigin::SourceAccount(
+						params.sender_account,
+					);
+
+					let message = ToRialtoMessagePayload {
+						spec_version: 0,
+						weight: params.size as _,
+						origin: dispatch_origin,
+						call: message_payload,
+						dispatch_fee_payment: DispatchFeePayment::AtSourceChain,
+					};
+					(message, pallet_bridge_messages::benchmarking::MESSAGE_FEE.into())
+				}
+
+				fn prepare_message_proof(
+					params: MessageProofParams,
+				) -> (rialto_messages::FromRialtoMessagesProof, Weight) {
+					use bp_messages::{MessageKey, storage_keys};
+					use bridge_runtime_common::{
+						messages::MessageBridge,
+						messages_benchmarking::{ed25519_sign, prepare_message_proof},
+					};
+					use codec::Encode;
+					use frame_support::weights::GetDispatchInfo;
+					use rialto_messages::WithRialtoMessageBridge;
+					use sp_runtime::traits::{Header, IdentifyAccount};
+
+					let remark = match params.size {
+						MessagesProofSize::Minimal(ref size) => vec![0u8; *size as _],
+						_ => vec![],
+					};
+					let call = Call::System(SystemCall::remark { remark });
+					let call_weight = call.get_dispatch_info().weight;
+
+					let rialto_account_id: bp_rialto::AccountId = Default::default();
+					let (millau_raw_public, millau_raw_signature) = ed25519_sign(
+						&call,
+						&rialto_account_id,
+						VERSION.spec_version,
+						bp_runtime::RIALTO_CHAIN_ID,
+						bp_runtime::MILLAU_CHAIN_ID,
+					);
+					let millau_public = MultiSigner::Ed25519(sp_core::ed25519::Public::from_raw(millau_raw_public));
+					let millau_signature = MultiSignature::Ed25519(sp_core::ed25519::Signature::from_raw(
+						millau_raw_signature,
+					));
+
+					if params.dispatch_fee_payment == DispatchFeePayment::AtTargetChain {
+						Self::endow_account(&millau_public.clone().into_account());
+					}
+
+					let make_rialto_message_key = |message_key: MessageKey| storage_keys::message_key(
+						<WithRialtoMessageBridge as MessageBridge>::BRIDGED_MESSAGES_PALLET_NAME,
+						&message_key.lane_id, message_key.nonce,
+					).0;
+					let make_rialto_outbound_lane_data_key = |lane_id| storage_keys::outbound_lane_data_key(
+						<WithRialtoMessageBridge as MessageBridge>::BRIDGED_MESSAGES_PALLET_NAME,
+						&lane_id,
+					).0;
+
+					let make_rialto_header = |state_root| bp_rialto::Header::new(
+						0,
+						Default::default(),
+						state_root,
+						Default::default(),
+						Default::default(),
+					);
+
+					let dispatch_fee_payment = params.dispatch_fee_payment.clone();
+					prepare_message_proof::<WithRialtoMessageBridge, bp_rialto::Hasher, Runtime, (), _, _, _>(
+						params,
+						make_rialto_message_key,
+						make_rialto_outbound_lane_data_key,
+						make_rialto_header,
+						call_weight,
+						bp_message_dispatch::MessagePayload {
+							spec_version: VERSION.spec_version,
+							weight: call_weight,
+							origin: bp_message_dispatch::CallOrigin::<
+								bp_rialto::AccountId,
+								MultiSigner,
+								Signature,
+							>::TargetAccount(
+								rialto_account_id,
+								millau_public,
+								millau_signature,
+							),
+							dispatch_fee_payment,
+							call: call.encode(),
+						}.encode(),
+					)
+				}
+
+				fn prepare_message_delivery_proof(
+					params: MessageDeliveryProofParams<Self::AccountId>,
+				) -> rialto_messages::ToRialtoMessagesDeliveryProof {
+					use bridge_runtime_common::messages_benchmarking::prepare_message_delivery_proof;
+					use rialto_messages::WithRialtoMessageBridge;
+					use sp_runtime::traits::Header;
+
+					prepare_message_delivery_proof::<WithRialtoMessageBridge, bp_rialto::Hasher, Runtime, (), _, _>(
+						params,
+						|lane_id| bp_messages::storage_keys::inbound_lane_data_key(
+							<WithRialtoMessageBridge as MessageBridge>::BRIDGED_MESSAGES_PALLET_NAME,
+							&lane_id,
+						).0,
+						|state_root| bp_rialto::Header::new(
+							0,
+							Default::default(),
+							state_root,
+							Default::default(),
+							Default::default(),
+						),
+					)
+				}
+
+				fn is_message_dispatched(nonce: bp_messages::MessageNonce) -> bool {
+					frame_system::Pallet::<Runtime>::events()
+						.into_iter()
+						.map(|event_record| event_record.event)
+						.any(|event| matches!(
+							event,
+							Event::BridgeDispatch(pallet_bridge_dispatch::Event::<Runtime, _>::MessageDispatched(
+								_, ([0, 0, 0, 0], nonce_from_event), _,
+							)) if nonce_from_event == nonce
+						))
+				}
+			}
+
 			use pallet_bridge_token_swap::benchmarking::Config as TokenSwapConfig;
 
 			impl TokenSwapConfig<WithRialtoTokenSwapInstance> for Runtime {
@@ -828,6 +1008,13 @@ impl_runtime_apis! {
 				}
 			}
 
+			add_benchmark!(
+				params,
+				batches,
+				pallet_bridge_messages,
+				MessagesBench::<Runtime, WithRialtoMessagesInstance>
+			);
+			add_benchmark!(params, batches, pallet_bridge_grandpa, BridgeRialtoGrandpa);
 			add_benchmark!(params, batches, pallet_bridge_token_swap, BridgeRialtoTokenSwap);
 
 			if batches.is_empty() { return Err("Benchmark not found for this pallet.".into()) }
@@ -868,8 +1055,7 @@ mod tests {
 
 	#[test]
 	fn ensure_millau_message_lane_weights_are_correct() {
-		// TODO: https://github.com/paritytech/parity-bridges-common/issues/390
-		type Weights = pallet_bridge_messages::weights::RialtoWeight<Runtime>;
+		type Weights = pallet_bridge_messages::weights::MillauWeight<Runtime>;
 
 		pallet_bridge_messages::ensure_weights_are_correct::<Weights>(
 			bp_millau::DEFAULT_MESSAGE_DELIVERY_TX_WEIGHT,
diff --git a/bridges/bin/millau/runtime/src/rialto_messages.rs b/bridges/bin/millau/runtime/src/rialto_messages.rs
index d46ab4ca04..4403c423c2 100644
--- a/bridges/bin/millau/runtime/src/rialto_messages.rs
+++ b/bridges/bin/millau/runtime/src/rialto_messages.rs
@@ -64,10 +64,10 @@ pub type FromRialtoMessagePayload =
 pub type FromRialtoEncodedCall = messages::target::FromBridgedChainEncodedMessageCall<crate::Call>;
 
 /// Messages proof for Rialto -> Millau messages.
-type FromRialtoMessagesProof = messages::target::FromBridgedChainMessagesProof<bp_rialto::Hash>;
+pub type FromRialtoMessagesProof = messages::target::FromBridgedChainMessagesProof<bp_rialto::Hash>;
 
 /// Messages delivery proof for Millau -> Rialto messages.
-type ToRialtoMessagesDeliveryProof =
+pub type ToRialtoMessagesDeliveryProof =
 	messages::source::FromBridgedChainMessagesDeliveryProof<bp_rialto::Hash>;
 
 /// Call-dispatch based message dispatch for Rialto -> Millau messages.
diff --git a/bridges/bin/rialto/runtime/src/lib.rs b/bridges/bin/rialto/runtime/src/lib.rs
index ab5318a4f7..a68de93069 100644
--- a/bridges/bin/rialto/runtime/src/lib.rs
+++ b/bridges/bin/rialto/runtime/src/lib.rs
@@ -399,21 +399,7 @@ parameter_types! {
 	/// Note that once this is hit the pallet will essentially throttle incoming requests down to one
 	/// call per block.
 	pub const MaxRequests: u32 = 50;
-}
 
-#[cfg(feature = "runtime-benchmarks")]
-parameter_types! {
-	/// Number of headers to keep in benchmarks.
-	///
-	/// In benchmarks we always populate with full number of `HeadersToKeep` to make sure that
-	/// pruning is taken into account.
-	///
-	/// Note: This is lower than regular value, to speed up benchmarking setup.
-	pub const HeadersToKeep: u32 = 1024;
-}
-
-#[cfg(not(feature = "runtime-benchmarks"))]
-parameter_types! {
 	/// Number of headers to keep.
 	///
 	/// Assuming the worst case of every header being finalized, we will keep headers at least for a
@@ -426,7 +412,7 @@ impl pallet_bridge_grandpa::Config for Runtime {
 	type BridgedChain = bp_millau::Millau;
 	type MaxRequests = MaxRequests;
 	type HeadersToKeep = HeadersToKeep;
-	type WeightInfo = pallet_bridge_grandpa::weights::RialtoWeight<Runtime>;
+	type WeightInfo = pallet_bridge_grandpa::weights::MillauWeight<Runtime>;
 }
 
 impl pallet_shift_session_manager::Config for Runtime {}
@@ -449,7 +435,7 @@ pub type WithMillauMessagesInstance = ();
 
 impl pallet_bridge_messages::Config<WithMillauMessagesInstance> for Runtime {
 	type Event = Event;
-	type WeightInfo = pallet_bridge_messages::weights::RialtoWeight<Runtime>;
+	type WeightInfo = pallet_bridge_messages::weights::MillauWeight<Runtime>;
 	type Parameter = millau_messages::RialtoToMillauMessagesParameter;
 	type MaxMessagesToPruneAtOnce = MaxMessagesToPruneAtOnce;
 	type MaxUnrewardedRelayerEntriesAtInboundLane = MaxUnrewardedRelayerEntriesAtInboundLane;
@@ -921,226 +907,6 @@ impl_runtime_apis! {
 			BridgeMillauMessages::inbound_unrewarded_relayers_state(lane)
 		}
 	}
-
-	#[cfg(feature = "runtime-benchmarks")]
-	impl frame_benchmarking::Benchmark<Block> for Runtime {
-		fn benchmark_metadata(extra: bool) -> (
-			Vec<frame_benchmarking::BenchmarkList>,
-			Vec<frame_support::traits::StorageInfo>,
-		) {
-			use frame_benchmarking::{list_benchmark, Benchmarking, BenchmarkList};
-			use frame_support::traits::StorageInfoTrait;
-
-			use pallet_bridge_messages::benchmarking::Pallet as MessagesBench;
-
-			let mut list = Vec::<BenchmarkList>::new();
-
-			list_benchmark!(list, extra, pallet_bridge_messages, MessagesBench::<Runtime, WithMillauMessagesInstance>);
-			list_benchmark!(list, extra, pallet_bridge_grandpa, BridgeMillauGrandpa);
-
-			let storage_info = AllPalletsWithSystem::storage_info();
-
-			return (list, storage_info)
-		}
-
-		fn dispatch_benchmark(
-			config: frame_benchmarking::BenchmarkConfig,
-		) -> Result<Vec<frame_benchmarking::BenchmarkBatch>, sp_runtime::RuntimeString> {
-			use frame_benchmarking::{Benchmarking, BenchmarkBatch, TrackedStorageKey, add_benchmark};
-
-			let whitelist: Vec<TrackedStorageKey> = vec![
-				// Block Number
-				hex_literal::hex!("26aa394eea5630e07c48ae0c9558cef702a5c1b19ab7a04f536c519aca4983ac").to_vec().into(),
-				// Execution Phase
-				hex_literal::hex!("26aa394eea5630e07c48ae0c9558cef7ff553b5a9862a516939d82b3d3d8661a").to_vec().into(),
-				// Event Count
-				hex_literal::hex!("26aa394eea5630e07c48ae0c9558cef70a98fdbe9ce6c55837576c60c7af3850").to_vec().into(),
-				// System Events
-				hex_literal::hex!("26aa394eea5630e07c48ae0c9558cef780d41e5e16056765bc8461851072c9d7").to_vec().into(),
-				// Caller 0 Account
-				hex_literal::hex!("26aa394eea5630e07c48ae0c9558cef7b99d880ec681799c0cf30e8886371da946c154ffd9992e395af90b5b13cc6f295c77033fce8a9045824a6690bbf99c6db269502f0a8d1d2a008542d5690a0749").to_vec().into(),
-			];
-
-			let mut batches = Vec::<BenchmarkBatch>::new();
-			let params = (&config, &whitelist);
-
-			use crate::millau_messages::{ToMillauMessagePayload, WithMillauMessageBridge};
-			use bp_runtime::messages::DispatchFeePayment;
-			use bridge_runtime_common::messages;
-			use pallet_bridge_messages::benchmarking::{
-				Pallet as MessagesBench,
-				Config as MessagesConfig,
-				MessageDeliveryProofParams,
-				MessageParams,
-				MessageProofParams,
-				ProofSize as MessagesProofSize,
-			};
-
-			impl MessagesConfig<WithMillauMessagesInstance> for Runtime {
-				fn maximal_message_size() -> u32 {
-					messages::source::maximal_message_size::<WithMillauMessageBridge>()
-				}
-
-				fn bridged_relayer_id() -> Self::InboundRelayer {
-					Default::default()
-				}
-
-				fn account_balance(account: &Self::AccountId) -> Self::OutboundMessageFee {
-					pallet_balances::Pallet::<Runtime>::free_balance(account)
-				}
-
-				fn endow_account(account: &Self::AccountId) {
-					pallet_balances::Pallet::<Runtime>::make_free_balance_be(
-						account,
-						Balance::MAX / 100,
-					);
-				}
-
-				fn prepare_outbound_message(
-					params: MessageParams<Self::AccountId>,
-				) -> (millau_messages::ToMillauMessagePayload, Balance) {
-					let message_payload = vec![0; params.size as usize];
-					let dispatch_origin = bp_message_dispatch::CallOrigin::SourceAccount(
-						params.sender_account,
-					);
-
-					let message = ToMillauMessagePayload {
-						spec_version: 0,
-						weight: params.size as _,
-						origin: dispatch_origin,
-						call: message_payload,
-						dispatch_fee_payment: DispatchFeePayment::AtSourceChain,
-					};
-					(message, pallet_bridge_messages::benchmarking::MESSAGE_FEE.into())
-				}
-
-				fn prepare_message_proof(
-					params: MessageProofParams,
-				) -> (millau_messages::FromMillauMessagesProof, Weight) {
-					use crate::millau_messages::WithMillauMessageBridge;
-					use bp_messages::{MessageKey, storage_keys};
-					use bridge_runtime_common::{
-						messages::MessageBridge,
-						messages_benchmarking::{ed25519_sign, prepare_message_proof},
-					};
-					use codec::Encode;
-					use frame_support::weights::GetDispatchInfo;
-					use sp_runtime::traits::{Header, IdentifyAccount};
-
-					let remark = match params.size {
-						MessagesProofSize::Minimal(ref size) => vec![0u8; *size as _],
-						_ => vec![],
-					};
-					let call = Call::System(SystemCall::remark { remark });
-					let call_weight = call.get_dispatch_info().weight;
-
-					let millau_account_id: bp_millau::AccountId = Default::default();
-					let (rialto_raw_public, rialto_raw_signature) = ed25519_sign(
-						&call,
-						&millau_account_id,
-						VERSION.spec_version,
-						bp_runtime::MILLAU_CHAIN_ID,
-						bp_runtime::RIALTO_CHAIN_ID,
-					);
-					let rialto_public = MultiSigner::Ed25519(sp_core::ed25519::Public::from_raw(rialto_raw_public));
-					let rialto_signature = MultiSignature::Ed25519(sp_core::ed25519::Signature::from_raw(
-						rialto_raw_signature,
-					));
-
-					if params.dispatch_fee_payment == DispatchFeePayment::AtTargetChain {
-						Self::endow_account(&rialto_public.clone().into_account());
-					}
-
-					let make_millau_message_key = |message_key: MessageKey| storage_keys::message_key(
-						<WithMillauMessageBridge as MessageBridge>::BRIDGED_MESSAGES_PALLET_NAME,
-						&message_key.lane_id, message_key.nonce,
-					).0;
-					let make_millau_outbound_lane_data_key = |lane_id| storage_keys::outbound_lane_data_key(
-						<WithMillauMessageBridge as MessageBridge>::BRIDGED_MESSAGES_PALLET_NAME,
-						&lane_id,
-					).0;
-
-					let make_millau_header = |state_root| bp_millau::Header::new(
-						0,
-						Default::default(),
-						state_root,
-						Default::default(),
-						Default::default(),
-					);
-
-					let dispatch_fee_payment = params.dispatch_fee_payment.clone();
-					prepare_message_proof::<WithMillauMessageBridge, bp_millau::Hasher, Runtime, (), _, _, _>(
-						params,
-						make_millau_message_key,
-						make_millau_outbound_lane_data_key,
-						make_millau_header,
-						call_weight,
-						bp_message_dispatch::MessagePayload {
-							spec_version: VERSION.spec_version,
-							weight: call_weight,
-							origin: bp_message_dispatch::CallOrigin::<
-								bp_millau::AccountId,
-								MultiSigner,
-								Signature,
-							>::TargetAccount(
-								millau_account_id,
-								rialto_public,
-								rialto_signature,
-							),
-							dispatch_fee_payment,
-							call: call.encode(),
-						}.encode(),
-					)
-				}
-
-				fn prepare_message_delivery_proof(
-					params: MessageDeliveryProofParams<Self::AccountId>,
-				) -> millau_messages::ToMillauMessagesDeliveryProof {
-					use crate::millau_messages::WithMillauMessageBridge;
-					use bridge_runtime_common::{messages_benchmarking::prepare_message_delivery_proof};
-					use sp_runtime::traits::Header;
-
-					prepare_message_delivery_proof::<WithMillauMessageBridge, bp_millau::Hasher, Runtime, (), _, _>(
-						params,
-						|lane_id| bp_messages::storage_keys::inbound_lane_data_key(
-							<WithMillauMessageBridge as MessageBridge>::BRIDGED_MESSAGES_PALLET_NAME,
-							&lane_id,
-						).0,
-						|state_root| bp_millau::Header::new(
-							0,
-							Default::default(),
-							state_root,
-							Default::default(),
-							Default::default(),
-						),
-					)
-				}
-
-				fn is_message_dispatched(nonce: bp_messages::MessageNonce) -> bool {
-					frame_system::Pallet::<Runtime>::events()
-						.into_iter()
-						.map(|event_record| event_record.event)
-						.any(|event| matches!(
-							event,
-							Event::BridgeDispatch(pallet_bridge_dispatch::Event::<Runtime, _>::MessageDispatched(
-								_, ([0, 0, 0, 0], nonce_from_event), _,
-							)) if nonce_from_event == nonce
-						))
-				}
-			}
-
-			add_benchmark!(
-				params,
-				batches,
-				pallet_bridge_messages,
-				MessagesBench::<Runtime, WithMillauMessagesInstance>
-			);
-			add_benchmark!(params, batches, pallet_bridge_grandpa, BridgeMillauGrandpa);
-
-			if batches.is_empty() { return Err("Benchmark not found for this pallet.".into()) }
-			Ok(batches)
-		}
-	}
 }
 
 /// Millau account ownership digest from Rialto.
@@ -1175,7 +941,7 @@ mod tests {
 
 	#[test]
 	fn ensure_rialto_message_lane_weights_are_correct() {
-		type Weights = pallet_bridge_messages::weights::RialtoWeight<Runtime>;
+		type Weights = pallet_bridge_messages::weights::MillauWeight<Runtime>;
 
 		pallet_bridge_messages::ensure_weights_are_correct::<Weights>(
 			bp_rialto::DEFAULT_MESSAGE_DELIVERY_TX_WEIGHT,
diff --git a/bridges/modules/grandpa/src/weights.rs b/bridges/modules/grandpa/src/weights.rs
index c0cce2c525..2c4660160a 100644
--- a/bridges/modules/grandpa/src/weights.rs
+++ b/bridges/modules/grandpa/src/weights.rs
@@ -16,14 +16,14 @@
 
 //! Autogenerated weights for `pallet_bridge_grandpa`
 //!
-//! THIS FILE WAS AUTO-GENERATED USING THE SUBSTRATE BENCHMARK CLI VERSION 3.0.0
-//! DATE: 2021-06-03, STEPS: [50, ], REPEAT: 20
+//! THIS FILE WAS AUTO-GENERATED USING THE SUBSTRATE BENCHMARK CLI VERSION 4.0.0-dev
+//! DATE: 2021-12-28, STEPS: 50, REPEAT: 20
 //! LOW RANGE: [], HIGH RANGE: []
 //! EXECUTION: Some(Wasm), WASM-EXECUTION: Compiled
 //! CHAIN: Some("dev"), DB CACHE: 128
 
 // Executed Command:
-// target/release/rialto-bridge-node
+// target/release/millau-bridge-node
 // benchmark
 // --chain=dev
 // --steps=50
@@ -34,7 +34,7 @@
 // --wasm-execution=Compiled
 // --heap-pages=4096
 // --output=./modules/grandpa/src/weights.rs
-// --template=./.maintain/rialto-weight-template.hbs
+// --template=./.maintain/millau-weight-template.hbs
 
 #![allow(clippy::all)]
 #![allow(unused_parens)]
@@ -51,13 +51,13 @@ pub trait WeightInfo {
 	fn submit_finality_proof(p: u32, v: u32) -> Weight;
 }
 
-/// Weights for `pallet_bridge_grandpa` using the Rialto node and recommended hardware.
-pub struct RialtoWeight<T>(PhantomData<T>);
-impl<T: frame_system::Config> WeightInfo for RialtoWeight<T> {
+/// Weights for `pallet_bridge_grandpa` using the Millau node and recommended hardware.
+pub struct MillauWeight<T>(PhantomData<T>);
+impl<T: frame_system::Config> WeightInfo for MillauWeight<T> {
 	fn submit_finality_proof(p: u32, v: u32) -> Weight {
-		(0 as Weight)
-			.saturating_add((59_692_000 as Weight).saturating_mul(p as Weight))
-			.saturating_add((6_876_000 as Weight).saturating_mul(v as Weight))
+		(115_651_000 as Weight)
+			.saturating_add((61_465_000 as Weight).saturating_mul(p as Weight))
+			.saturating_add((3_438_000 as Weight).saturating_mul(v as Weight))
 			.saturating_add(T::DbWeight::get().reads(7 as Weight))
 			.saturating_add(T::DbWeight::get().writes(6 as Weight))
 	}
@@ -66,9 +66,9 @@ impl<T: frame_system::Config> WeightInfo for RialtoWeight<T> {
 // For backwards compatibility and tests
 impl WeightInfo for () {
 	fn submit_finality_proof(p: u32, v: u32) -> Weight {
-		(0 as Weight)
-			.saturating_add((59_692_000 as Weight).saturating_mul(p as Weight))
-			.saturating_add((6_876_000 as Weight).saturating_mul(v as Weight))
+		(115_651_000 as Weight)
+			.saturating_add((61_465_000 as Weight).saturating_mul(p as Weight))
+			.saturating_add((3_438_000 as Weight).saturating_mul(v as Weight))
 			.saturating_add(RocksDbWeight::get().reads(7 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(6 as Weight))
 	}
diff --git a/bridges/modules/messages/src/weights.rs b/bridges/modules/messages/src/weights.rs
index 9dce11168f..7c5df201f9 100644
--- a/bridges/modules/messages/src/weights.rs
+++ b/bridges/modules/messages/src/weights.rs
@@ -16,14 +16,14 @@
 
 //! Autogenerated weights for `pallet_bridge_messages`
 //!
-//! THIS FILE WAS AUTO-GENERATED USING THE SUBSTRATE BENCHMARK CLI VERSION 3.0.0
-//! DATE: 2021-06-18, STEPS: [50, ], REPEAT: 20
+//! THIS FILE WAS AUTO-GENERATED USING THE SUBSTRATE BENCHMARK CLI VERSION 4.0.0-dev
+//! DATE: 2021-12-28, STEPS: 50, REPEAT: 20
 //! LOW RANGE: [], HIGH RANGE: []
 //! EXECUTION: Some(Wasm), WASM-EXECUTION: Compiled
 //! CHAIN: Some("dev"), DB CACHE: 128
 
 // Executed Command:
-// target/release/rialto-bridge-node
+// target/release/millau-bridge-node
 // benchmark
 // --chain=dev
 // --steps=50
@@ -34,7 +34,7 @@
 // --wasm-execution=Compiled
 // --heap-pages=4096
 // --output=./modules/messages/src/weights.rs
-// --template=./.maintain/rialto-weight-template.hbs
+// --template=./.maintain/millau-weight-template.hbs
 
 #![allow(clippy::all)]
 #![allow(unused_parens)]
@@ -71,120 +71,120 @@ pub trait WeightInfo {
 	fn receive_delivery_proof_for_multiple_messages_by_multiple_relayers(i: u32) -> Weight;
 }
 
-/// Weights for `pallet_bridge_messages` using the Rialto node and recommended hardware.
-pub struct RialtoWeight<T>(PhantomData<T>);
-impl<T: frame_system::Config> WeightInfo for RialtoWeight<T> {
+/// Weights for `pallet_bridge_messages` using the Millau node and recommended hardware.
+pub struct MillauWeight<T>(PhantomData<T>);
+impl<T: frame_system::Config> WeightInfo for MillauWeight<T> {
 	fn send_minimal_message_worst_case() -> Weight {
-		(159_305_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(117_480_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(7 as Weight))
 			.saturating_add(T::DbWeight::get().writes(12 as Weight))
 	}
 	fn send_1_kb_message_worst_case() -> Weight {
-		(164_394_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(128_391_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(7 as Weight))
 			.saturating_add(T::DbWeight::get().writes(12 as Weight))
 	}
 	fn send_16_kb_message_worst_case() -> Weight {
-		(223_521_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(149_149_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(7 as Weight))
 			.saturating_add(T::DbWeight::get().writes(12 as Weight))
 	}
 	fn maximal_increase_message_fee() -> Weight {
-		(6_781_470_000 as Weight)
+		(6_015_058_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(5 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn increase_message_fee(i: u32) -> Weight {
-		(114_963_000 as Weight)
-			.saturating_add((6_000 as Weight).saturating_mul(i as Weight))
+		(0 as Weight)
+			.saturating_add((2_000 as Weight).saturating_mul(i as Weight))
 			.saturating_add(T::DbWeight::get().reads(5 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof() -> Weight {
-		(206_769_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(179_892_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_two_messages_proof() -> Weight {
-		(343_982_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(291_793_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof_with_outbound_lane_state() -> Weight {
-		(223_738_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(192_191_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof_1_kb() -> Weight {
-		(235_369_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(202_104_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof_16_kb() -> Weight {
-		(510_338_000 as Weight)
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(357_144_000 as Weight)
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_prepaid_message_proof() -> Weight {
-		(141_536_000 as Weight)
+		(122_648_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(3 as Weight))
 			.saturating_add(T::DbWeight::get().writes(1 as Weight))
 	}
 	fn receive_delivery_proof_for_single_message() -> Weight {
-		(128_805_000 as Weight)
+		(107_631_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_two_messages_by_single_relayer() -> Weight {
-		(137_143_000 as Weight)
+		(113_885_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(7 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_two_messages_by_two_relayers() -> Weight {
-		(193_108_000 as Weight)
+		(155_151_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(8 as Weight))
 			.saturating_add(T::DbWeight::get().writes(4 as Weight))
 	}
 	fn send_messages_of_various_lengths(i: u32) -> Weight {
-		(133_632_000 as Weight)
-			.saturating_add((4_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(0 as Weight)
+			.saturating_add((2_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(T::DbWeight::get().reads(7 as Weight))
 			.saturating_add(T::DbWeight::get().writes(12 as Weight))
 	}
 	fn receive_multiple_messages_proof(i: u32) -> Weight {
-		(0 as Weight)
-			.saturating_add((145_006_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(56_209_000 as Weight)
+			.saturating_add((109_502_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_message_proofs_with_extra_nodes(i: u32) -> Weight {
-		(486_301_000 as Weight)
-			.saturating_add((10_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(0 as Weight)
+			.saturating_add((5_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_message_proofs_with_large_leaf(i: u32) -> Weight {
-		(178_139_000 as Weight)
-			.saturating_add((7_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(50_281_000 as Weight)
+			.saturating_add((2_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_multiple_messages_proof_with_outbound_lane_state(i: u32) -> Weight {
-		(0 as Weight)
-			.saturating_add((150_844_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(T::DbWeight::get().reads(5 as Weight))
+		(70_297_000 as Weight)
+			.saturating_add((110_892_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(T::DbWeight::get().reads(6 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_multiple_messages_by_single_relayer(i: u32) -> Weight {
-		(113_140_000 as Weight)
-			.saturating_add((7_656_000 as Weight).saturating_mul(i as Weight))
+		(0 as Weight)
+			.saturating_add((8_016_000 as Weight).saturating_mul(i as Weight))
 			.saturating_add(T::DbWeight::get().reads(5 as Weight))
 			.saturating_add(T::DbWeight::get().reads((1 as Weight).saturating_mul(i as Weight)))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_multiple_messages_by_multiple_relayers(i: u32) -> Weight {
-		(97_424_000 as Weight)
-			.saturating_add((63_128_000 as Weight).saturating_mul(i as Weight))
+		(0 as Weight)
+			.saturating_add((50_981_000 as Weight).saturating_mul(i as Weight))
 			.saturating_add(T::DbWeight::get().reads(5 as Weight))
 			.saturating_add(T::DbWeight::get().reads((2 as Weight).saturating_mul(i as Weight)))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
@@ -195,116 +195,116 @@ impl<T: frame_system::Config> WeightInfo for RialtoWeight<T> {
 // For backwards compatibility and tests
 impl WeightInfo for () {
 	fn send_minimal_message_worst_case() -> Weight {
-		(159_305_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(117_480_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(7 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(12 as Weight))
 	}
 	fn send_1_kb_message_worst_case() -> Weight {
-		(164_394_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(128_391_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(7 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(12 as Weight))
 	}
 	fn send_16_kb_message_worst_case() -> Weight {
-		(223_521_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(149_149_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(7 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(12 as Weight))
 	}
 	fn maximal_increase_message_fee() -> Weight {
-		(6_781_470_000 as Weight)
+		(6_015_058_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn increase_message_fee(i: u32) -> Weight {
-		(114_963_000 as Weight)
-			.saturating_add((6_000 as Weight).saturating_mul(i as Weight))
+		(0 as Weight)
+			.saturating_add((2_000 as Weight).saturating_mul(i as Weight))
 			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof() -> Weight {
-		(206_769_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(179_892_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_two_messages_proof() -> Weight {
-		(343_982_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(291_793_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof_with_outbound_lane_state() -> Weight {
-		(223_738_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(192_191_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof_1_kb() -> Weight {
-		(235_369_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(202_104_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_message_proof_16_kb() -> Weight {
-		(510_338_000 as Weight)
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(357_144_000 as Weight)
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_single_prepaid_message_proof() -> Weight {
-		(141_536_000 as Weight)
+		(122_648_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(3 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(1 as Weight))
 	}
 	fn receive_delivery_proof_for_single_message() -> Weight {
-		(128_805_000 as Weight)
+		(107_631_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_two_messages_by_single_relayer() -> Weight {
-		(137_143_000 as Weight)
+		(113_885_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(7 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_two_messages_by_two_relayers() -> Weight {
-		(193_108_000 as Weight)
+		(155_151_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(8 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(4 as Weight))
 	}
 	fn send_messages_of_various_lengths(i: u32) -> Weight {
-		(133_632_000 as Weight)
-			.saturating_add((4_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(0 as Weight)
+			.saturating_add((2_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(RocksDbWeight::get().reads(7 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(12 as Weight))
 	}
 	fn receive_multiple_messages_proof(i: u32) -> Weight {
-		(0 as Weight)
-			.saturating_add((145_006_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(56_209_000 as Weight)
+			.saturating_add((109_502_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_message_proofs_with_extra_nodes(i: u32) -> Weight {
-		(486_301_000 as Weight)
-			.saturating_add((10_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(0 as Weight)
+			.saturating_add((5_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_message_proofs_with_large_leaf(i: u32) -> Weight {
-		(178_139_000 as Weight)
-			.saturating_add((7_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(50_281_000 as Weight)
+			.saturating_add((2_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_multiple_messages_proof_with_outbound_lane_state(i: u32) -> Weight {
-		(0 as Weight)
-			.saturating_add((150_844_000 as Weight).saturating_mul(i as Weight))
-			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
+		(70_297_000 as Weight)
+			.saturating_add((110_892_000 as Weight).saturating_mul(i as Weight))
+			.saturating_add(RocksDbWeight::get().reads(6 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_multiple_messages_by_single_relayer(i: u32) -> Weight {
-		(113_140_000 as Weight)
-			.saturating_add((7_656_000 as Weight).saturating_mul(i as Weight))
+		(0 as Weight)
+			.saturating_add((8_016_000 as Weight).saturating_mul(i as Weight))
 			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
 			.saturating_add(RocksDbWeight::get().reads((1 as Weight).saturating_mul(i as Weight)))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn receive_delivery_proof_for_multiple_messages_by_multiple_relayers(i: u32) -> Weight {
-		(97_424_000 as Weight)
-			.saturating_add((63_128_000 as Weight).saturating_mul(i as Weight))
+		(0 as Weight)
+			.saturating_add((50_981_000 as Weight).saturating_mul(i as Weight))
 			.saturating_add(RocksDbWeight::get().reads(5 as Weight))
 			.saturating_add(RocksDbWeight::get().reads((2 as Weight).saturating_mul(i as Weight)))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
diff --git a/bridges/modules/messages/src/weights_ext.rs b/bridges/modules/messages/src/weights_ext.rs
index fef09c6ceb..483a22eda1 100644
--- a/bridges/modules/messages/src/weights_ext.rs
+++ b/bridges/modules/messages/src/weights_ext.rs
@@ -390,7 +390,7 @@ impl WeightInfoExt for () {
 	}
 }
 
-impl<T: frame_system::Config> WeightInfoExt for crate::weights::RialtoWeight<T> {
+impl<T: frame_system::Config> WeightInfoExt for crate::weights::MillauWeight<T> {
 	fn expected_extra_storage_proof_size() -> u32 {
 		EXTRA_STORAGE_PROOF_SIZE
 	}
diff --git a/bridges/modules/token-swap/src/benchmarking.rs b/bridges/modules/token-swap/src/benchmarking.rs
index bbc544a8b9..6ca35f5f39 100644
--- a/bridges/modules/token-swap/src/benchmarking.rs
+++ b/bridges/modules/token-swap/src/benchmarking.rs
@@ -30,7 +30,7 @@ use frame_system::RawOrigin;
 use sp_core::H256;
 use sp_io::hashing::blake2_256;
 use sp_runtime::traits::Bounded;
-use sp_std::vec::Vec;
+use sp_std::{boxed::Box, vec::Vec};
 
 const SEED: u32 = 0;
 
diff --git a/bridges/modules/token-swap/src/weights.rs b/bridges/modules/token-swap/src/weights.rs
index 06cb6b85cf..51c5d99de9 100644
--- a/bridges/modules/token-swap/src/weights.rs
+++ b/bridges/modules/token-swap/src/weights.rs
@@ -17,7 +17,7 @@
 //! Autogenerated weights for `pallet_bridge_token_swap`
 //!
 //! THIS FILE WAS AUTO-GENERATED USING THE SUBSTRATE BENCHMARK CLI VERSION 4.0.0-dev
-//! DATE: 2021-10-06, STEPS: 50, REPEAT: 20
+//! DATE: 2021-12-28, STEPS: 50, REPEAT: 20
 //! LOW RANGE: [], HIGH RANGE: []
 //! EXECUTION: Some(Wasm), WASM-EXECUTION: Compiled
 //! CHAIN: Some("dev"), DB CACHE: 128
@@ -57,17 +57,17 @@ pub trait WeightInfo {
 pub struct MillauWeight<T>(PhantomData<T>);
 impl<T: frame_system::Config> WeightInfo for MillauWeight<T> {
 	fn create_swap() -> Weight {
-		(116_040_000 as Weight)
+		(90_368_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(3 as Weight))
 			.saturating_add(T::DbWeight::get().writes(4 as Weight))
 	}
 	fn claim_swap() -> Weight {
-		(102_882_000 as Weight)
+		(88_397_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(3 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
 	fn cancel_swap() -> Weight {
-		(99_434_000 as Weight)
+		(91_253_000 as Weight)
 			.saturating_add(T::DbWeight::get().reads(3 as Weight))
 			.saturating_add(T::DbWeight::get().writes(3 as Weight))
 	}
@@ -76,17 +76,17 @@ impl<T: frame_system::Config> WeightInfo for MillauWeight<T> {
 // For backwards compatibility and tests
 impl WeightInfo for () {
 	fn create_swap() -> Weight {
-		(116_040_000 as Weight)
+		(90_368_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(3 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(4 as Weight))
 	}
 	fn claim_swap() -> Weight {
-		(102_882_000 as Weight)
+		(88_397_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(3 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
 	fn cancel_swap() -> Weight {
-		(99_434_000 as Weight)
+		(91_253_000 as Weight)
 			.saturating_add(RocksDbWeight::get().reads(3 as Weight))
 			.saturating_add(RocksDbWeight::get().writes(3 as Weight))
 	}
diff --git a/bridges/primitives/chain-millau/src/lib.rs b/bridges/primitives/chain-millau/src/lib.rs
index 2f51320dc8..6a8bbd3e33 100644
--- a/bridges/primitives/chain-millau/src/lib.rs
+++ b/bridges/primitives/chain-millau/src/lib.rs
@@ -103,7 +103,7 @@ pub const MAX_SINGLE_MESSAGE_DELIVERY_CONFIRMATION_TX_WEIGHT: Weight = 2_000_000
 /// chain. Don't put too much reserve there, because it is used to **decrease**
 /// `DEFAULT_MESSAGE_DELIVERY_TX_WEIGHT` cost. So putting large reserve would make delivery
 /// transactions cheaper.
-pub const PAY_INBOUND_DISPATCH_FEE_WEIGHT: Weight = 600_000_000;
+pub const PAY_INBOUND_DISPATCH_FEE_WEIGHT: Weight = 700_000_000;
 
 /// The target length of a session (how often authorities change) on Millau measured in of number of
 /// blocks.
diff --git a/bridges/primitives/chain-rialto/src/lib.rs b/bridges/primitives/chain-rialto/src/lib.rs
index 4fd7cbb463..b995410a65 100644
--- a/bridges/primitives/chain-rialto/src/lib.rs
+++ b/bridges/primitives/chain-rialto/src/lib.rs
@@ -94,7 +94,7 @@ pub const MAX_SINGLE_MESSAGE_DELIVERY_CONFIRMATION_TX_WEIGHT: Weight = 2_000_000
 /// chain. Don't put too much reserve there, because it is used to **decrease**
 /// `DEFAULT_MESSAGE_DELIVERY_TX_WEIGHT` cost. So putting large reserve would make delivery
 /// transactions cheaper.
-pub const PAY_INBOUND_DISPATCH_FEE_WEIGHT: Weight = 600_000_000;
+pub const PAY_INBOUND_DISPATCH_FEE_WEIGHT: Weight = 700_000_000;
 
 /// The target length of a session (how often authorities change) on Rialto measured in of number of
 /// blocks.
diff --git a/bridges/relays/bin-substrate/src/chains/kusama_headers_to_polkadot.rs b/bridges/relays/bin-substrate/src/chains/kusama_headers_to_polkadot.rs
index c36c336718..13d9f12141 100644
--- a/bridges/relays/bin-substrate/src/chains/kusama_headers_to_polkadot.rs
+++ b/bridges/relays/bin-substrate/src/chains/kusama_headers_to_polkadot.rs
@@ -83,7 +83,7 @@ pub(crate) mod tests {
 		// differ from the `DbWeight` of Rialto runtime. But now (and most probably forever) it is
 		// the same.
 		type GrandpaPalletWeights =
-			pallet_bridge_grandpa::weights::RialtoWeight<rialto_runtime::Runtime>;
+			pallet_bridge_grandpa::weights::MillauWeight<rialto_runtime::Runtime>;
 
 		// The following formula shall not be treated as super-accurate - guard is to protect from
 		// mad relays, not to protect from over-average loses.
diff --git a/bridges/relays/lib-substrate-relay/src/messages_lane.rs b/bridges/relays/lib-substrate-relay/src/messages_lane.rs
index 4742ce6e48..87146be489 100644
--- a/bridges/relays/lib-substrate-relay/src/messages_lane.rs
+++ b/bridges/relays/lib-substrate-relay/src/messages_lane.rs
@@ -453,7 +453,7 @@ mod tests {
 	use bp_runtime::Chain;
 
 	type RialtoToMillauMessagesWeights =
-		pallet_bridge_messages::weights::RialtoWeight<rialto_runtime::Runtime>;
+		pallet_bridge_messages::weights::MillauWeight<rialto_runtime::Runtime>;
 
 	#[test]
 	fn select_delivery_transaction_limits_works() {
@@ -469,7 +469,7 @@ mod tests {
 			// i.e. weight reserved for messages dispatch allows dispatch of non-trivial messages.
 			//
 			// Any significant change in this values should attract additional attention.
-			(782, 216_583_333_334),
+			(958, 216_583_333_334),
 		);
 	}
 }