diff --git a/bin/millau/runtime/src/lib.rs b/bin/millau/runtime/src/lib.rs
index b1f1e33d18a47..d6e99afb2d8bb 100644
--- a/bin/millau/runtime/src/lib.rs
+++ b/bin/millau/runtime/src/lib.rs
@@ -62,7 +62,7 @@ pub use frame_support::{
 	construct_runtime,
 	dispatch::DispatchClass,
 	parameter_types,
-	traits::{Currency, ExistenceRequirement, Imbalance, KeyOwnerProofSystem},
+	traits::{ConstU32, ConstU8, Currency, ExistenceRequirement, Imbalance, KeyOwnerProofSystem},
 	weights::{
 		constants::WEIGHT_PER_SECOND, ConstantMultiplier, IdentityFee, RuntimeDbWeight, Weight,
 	},
@@ -215,19 +215,15 @@ impl frame_system::Config for Runtime {
 
 impl pallet_randomness_collective_flip::Config for Runtime {}
 
-parameter_types! {
-	pub const MaxAuthorities: u32 = 10;
-}
-
 impl pallet_aura::Config for Runtime {
 	type AuthorityId = AuraId;
-	type MaxAuthorities = MaxAuthorities;
+	type MaxAuthorities = ConstU32<10>;
 	type DisabledValidators = ();
 }
 
 impl pallet_beefy::Config for Runtime {
 	type BeefyId = BeefyId;
-	type MaxAuthorities = MaxAuthorities;
+	type MaxAuthorities = ConstU32<10>;
 	type OnNewValidatorSet = MmrLeaf;
 }
 
@@ -243,7 +239,7 @@ impl pallet_grandpa::Config for Runtime {
 	type HandleEquivocation = ();
 	// TODO: update me (https://github.com/paritytech/parity-bridges-common/issues/78)
 	type WeightInfo = ();
-	type MaxAuthorities = MaxAuthorities;
+	type MaxAuthorities = ConstU32<10>;
 }
 
 /// MMR helper types.
@@ -311,10 +307,6 @@ impl pallet_timestamp::Config for Runtime {
 
 parameter_types! {
 	pub const ExistentialDeposit: bp_millau::Balance = 500;
-	// For weight estimation, we assume that the most locks on an individual account will be 50.
-	// This number may need to be adjusted in the future if this assumption no longer holds true.
-	pub const MaxLocks: u32 = 50;
-	pub const MaxReserves: u32 = 50;
 }
 
 impl pallet_balances::Config for Runtime {
@@ -327,15 +319,16 @@ impl pallet_balances::Config for Runtime {
 	type AccountStore = System;
 	// TODO: update me (https://github.com/paritytech/parity-bridges-common/issues/78)
 	type WeightInfo = ();
-	type MaxLocks = MaxLocks;
-	type MaxReserves = MaxReserves;
+	// For weight estimation, we assume that the most locks on an individual account will be 50.
+	// This number may need to be adjusted in the future if this assumption no longer holds true.
+	type MaxLocks = ConstU32<50>;
+	type MaxReserves = ConstU32<50>;
 	type ReserveIdentifier = [u8; 8];
 }
 
 parameter_types! {
 	pub const TransactionBaseFee: Balance = 0;
 	pub const TransactionByteFee: Balance = 1;
-	pub const OperationalFeeMultiplier: u8 = 5;
 	// values for following parameters are copied from polkadot repo, but it is fine
 	// not to sync them - we're not going to make Rialto a full copy of one of Polkadot-like chains
 	pub const TargetBlockFullness: Perquintill = Perquintill::from_percent(25);
@@ -346,7 +339,7 @@ parameter_types! {
 
 impl pallet_transaction_payment::Config for Runtime {
 	type OnChargeTransaction = pallet_transaction_payment::CurrencyAdapter<Balances, ()>;
-	type OperationalFeeMultiplier = OperationalFeeMultiplier;
+	type OperationalFeeMultiplier = ConstU8<5>;
 	type WeightToFee = bp_millau::WeightToFee;
 	type LengthToFee = ConstantMultiplier<Balance, TransactionByteFee>;
 	type FeeMultiplierUpdate = pallet_transaction_payment::TargetedFeeAdjustment<
@@ -383,14 +376,6 @@ impl pallet_session::Config for Runtime {
 	type WeightInfo = ();
 }
 
-parameter_types! {
-	// This is a pretty unscientific cap.
-	//
-	// Note that once this is hit the pallet will essentially throttle incoming requests down to one
-	// call per block.
-	pub const MaxRequests: u32 = 50;
-}
-
 impl pallet_bridge_relayers::Config for Runtime {
 	type RuntimeEvent = RuntimeEvent;
 	type Reward = Balance;
@@ -439,7 +424,11 @@ parameter_types! {
 pub type RialtoGrandpaInstance = ();
 impl pallet_bridge_grandpa::Config for Runtime {
 	type BridgedChain = bp_rialto::Rialto;
-	type MaxRequests = MaxRequests;
+	// This is a pretty unscientific cap.
+	//
+	// Note that once this is hit the pallet will essentially throttle incoming requests down to one
+	// call per block.
+	type MaxRequests = ConstU32<50>;
 	type HeadersToKeep = HeadersToKeep;
 	type MaxBridgedAuthorities = MaxAuthoritiesAtRialto;
 	type MaxBridgedHeaderSize = MaxRialtoHeaderSize;
@@ -450,7 +439,7 @@ impl pallet_bridge_grandpa::Config for Runtime {
 pub type WestendGrandpaInstance = pallet_bridge_grandpa::Instance1;
 impl pallet_bridge_grandpa::Config<WestendGrandpaInstance> for Runtime {
 	type BridgedChain = bp_westend::Westend;
-	type MaxRequests = MaxRequests;
+	type MaxRequests = ConstU32<50>;
 	type HeadersToKeep = HeadersToKeep;
 	type MaxBridgedAuthorities = MaxAuthoritiesAtWestend;
 	type MaxBridgedHeaderSize = MaxWestendHeaderSize;
diff --git a/bin/millau/runtime/src/xcm_config.rs b/bin/millau/runtime/src/xcm_config.rs
index b5be117ac7732..a3a59e626e572 100644
--- a/bin/millau/runtime/src/xcm_config.rs
+++ b/bin/millau/runtime/src/xcm_config.rs
@@ -31,7 +31,7 @@ use bridge_runtime_common::{
 };
 use frame_support::{
 	parameter_types,
-	traits::{Everything, Nothing},
+	traits::{ConstU32, Everything, Nothing},
 };
 use xcm::latest::prelude::*;
 use xcm_builder::{
@@ -112,10 +112,6 @@ pub type XcmRouter = (
 	XcmBridgeAdapter<ToRialtoParachainBridge>,
 );
 
-parameter_types! {
-	pub const MaxAssetsIntoHolding: u32 = 64;
-}
-
 /// The barriers one of which must be passed for an XCM message to be executed.
 pub type Barrier = (
 	// Weight that is paid for may be consumed.
@@ -149,7 +145,7 @@ impl xcm_executor::Config for XcmConfig {
 	type AssetClaims = XcmPallet;
 	type SubscriptionService = XcmPallet;
 	type PalletInstancesInfo = AllPalletsWithSystem;
-	type MaxAssetsIntoHolding = MaxAssetsIntoHolding;
+	type MaxAssetsIntoHolding = ConstU32<64>;
 	type FeeManager = ();
 	type MessageExporter = ();
 	type UniversalAliases = Nothing;
diff --git a/bin/rialto-parachain/runtime/src/lib.rs b/bin/rialto-parachain/runtime/src/lib.rs
index f946abf4c1da9..2d0be49a07f46 100644
--- a/bin/rialto-parachain/runtime/src/lib.rs
+++ b/bin/rialto-parachain/runtime/src/lib.rs
@@ -50,7 +50,7 @@ pub use frame_support::{
 	construct_runtime,
 	dispatch::DispatchClass,
 	match_types, parameter_types,
-	traits::{Everything, IsInVec, Nothing, Randomness},
+	traits::{ConstU32, Everything, IsInVec, Nothing, Randomness},
 	weights::{
 		constants::{BlockExecutionWeight, ExtrinsicBaseWeight, RocksDbWeight, WEIGHT_PER_SECOND},
 		IdentityFee, Weight,
@@ -249,8 +249,6 @@ parameter_types! {
 	pub const CreationFee: u128 = MILLIUNIT;
 	pub const TransactionByteFee: u128 = MICROUNIT;
 	pub const OperationalFeeMultiplier: u8 = 5;
-	pub const MaxLocks: u32 = 50;
-	pub const MaxReserves: u32 = 50;
 }
 
 impl pallet_balances::Config for Runtime {
@@ -262,8 +260,8 @@ impl pallet_balances::Config for Runtime {
 	type ExistentialDeposit = ExistentialDeposit;
 	type AccountStore = System;
 	type WeightInfo = pallet_balances::weights::SubstrateWeight<Runtime>;
-	type MaxLocks = MaxLocks;
-	type MaxReserves = MaxReserves;
+	type MaxLocks = ConstU32<50>;
+	type MaxReserves = ConstU32<50>;
 	type ReserveIdentifier = [u8; 8];
 }
 
@@ -518,12 +516,6 @@ impl pallet_bridge_relayers::Config for Runtime {
 }
 
 parameter_types! {
-	/// This is a pretty unscientific cap.
-	///
-	/// 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 at least for a
@@ -539,7 +531,11 @@ parameter_types! {
 pub type MillauGrandpaInstance = ();
 impl pallet_bridge_grandpa::Config for Runtime {
 	type BridgedChain = bp_millau::Millau;
-	type MaxRequests = MaxRequests;
+	/// This is a pretty unscientific cap.
+	///
+	/// Note that once this is hit the pallet will essentially throttle incoming requests down to
+	/// one call per block.
+	type MaxRequests = ConstU32<50>;
 	type HeadersToKeep = HeadersToKeep;
 	type MaxBridgedAuthorities = MaxAuthoritiesAtMillau;
 	type MaxBridgedHeaderSize = MaxMillauHeaderSize;
diff --git a/bin/rialto/runtime/src/lib.rs b/bin/rialto/runtime/src/lib.rs
index 25778705e5ef5..59284df910a26 100644
--- a/bin/rialto/runtime/src/lib.rs
+++ b/bin/rialto/runtime/src/lib.rs
@@ -61,7 +61,7 @@ pub use frame_support::{
 	construct_runtime,
 	dispatch::DispatchClass,
 	parameter_types,
-	traits::{Currency, ExistenceRequirement, Imbalance, KeyOwnerProofSystem},
+	traits::{ConstU32, ConstU8, Currency, ExistenceRequirement, Imbalance, KeyOwnerProofSystem},
 	weights::{constants::WEIGHT_PER_SECOND, IdentityFee, RuntimeDbWeight, Weight},
 	StorageValue,
 };
@@ -222,13 +222,12 @@ pub const BABE_GENESIS_EPOCH_CONFIG: sp_consensus_babe::BabeEpochConfiguration =
 parameter_types! {
 	pub const EpochDuration: u64 = bp_rialto::EPOCH_DURATION_IN_SLOTS as u64;
 	pub const ExpectedBlockTime: bp_rialto::Moment = bp_rialto::time_units::MILLISECS_PER_BLOCK;
-	pub const MaxAuthorities: u32 = 10;
 }
 
 impl pallet_babe::Config for Runtime {
 	type EpochDuration = EpochDuration;
 	type ExpectedBlockTime = ExpectedBlockTime;
-	type MaxAuthorities = MaxAuthorities;
+	type MaxAuthorities = ConstU32<10>;
 
 	// session module is the trigger
 	type EpochChangeTrigger = pallet_babe::ExternalTrigger;
@@ -251,13 +250,13 @@ impl pallet_babe::Config for Runtime {
 
 impl pallet_beefy::Config for Runtime {
 	type BeefyId = BeefyId;
-	type MaxAuthorities = MaxAuthorities;
+	type MaxAuthorities = ConstU32<10>;
 	type OnNewValidatorSet = MmrLeaf;
 }
 
 impl pallet_grandpa::Config for Runtime {
 	type RuntimeEvent = RuntimeEvent;
-	type MaxAuthorities = MaxAuthorities;
+	type MaxAuthorities = ConstU32<10>;
 	type KeyOwnerProofSystem = ();
 	type KeyOwnerProof =
 		<Self::KeyOwnerProofSystem as KeyOwnerProofSystem<(KeyTypeId, GrandpaId)>>::Proof;
@@ -327,10 +326,6 @@ impl pallet_timestamp::Config for Runtime {
 
 parameter_types! {
 	pub const ExistentialDeposit: bp_rialto::Balance = 500;
-	// For weight estimation, we assume that the most locks on an individual account will be 50.
-	// This number may need to be adjusted in the future if this assumption no longer holds true.
-	pub const MaxLocks: u32 = 50;
-	pub const MaxReserves: u32 = 50;
 }
 
 impl pallet_balances::Config for Runtime {
@@ -343,15 +338,16 @@ impl pallet_balances::Config for Runtime {
 	type AccountStore = System;
 	// TODO: update me (https://github.com/paritytech/parity-bridges-common/issues/78)
 	type WeightInfo = ();
-	type MaxLocks = MaxLocks;
-	type MaxReserves = MaxReserves;
+	// For weight estimation, we assume that the most locks on an individual account will be 50.
+	// This number may need to be adjusted in the future if this assumption no longer holds true.
+	type MaxLocks = ConstU32<50>;
+	type MaxReserves = ConstU32<50>;
 	type ReserveIdentifier = [u8; 8];
 }
 
 parameter_types! {
 	pub const TransactionBaseFee: Balance = 0;
 	pub const TransactionByteFee: Balance = 1;
-	pub const OperationalFeeMultiplier: u8 = 5;
 	// values for following parameters are copied from polkadot repo, but it is fine
 	// not to sync them - we're not going to make Rialto a full copy of one of Polkadot-like chains
 	pub const TargetBlockFullness: Perquintill = Perquintill::from_percent(25);
@@ -362,7 +358,7 @@ parameter_types! {
 
 impl pallet_transaction_payment::Config for Runtime {
 	type OnChargeTransaction = pallet_transaction_payment::CurrencyAdapter<Balances, ()>;
-	type OperationalFeeMultiplier = OperationalFeeMultiplier;
+	type OperationalFeeMultiplier = ConstU8<5>;
 	type WeightToFee = bp_rialto::WeightToFee;
 	type LengthToFee = bp_rialto::WeightToFee;
 	type FeeMultiplierUpdate = pallet_transaction_payment::TargetedFeeAdjustment<
@@ -394,7 +390,7 @@ impl pallet_session::Config for Runtime {
 }
 
 impl pallet_authority_discovery::Config for Runtime {
-	type MaxAuthorities = MaxAuthorities;
+	type MaxAuthorities = ConstU32<10>;
 }
 
 impl pallet_bridge_relayers::Config for Runtime {
@@ -405,12 +401,6 @@ impl pallet_bridge_relayers::Config for Runtime {
 }
 
 parameter_types! {
-	/// This is a pretty unscientific cap.
-	///
-	/// 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 at least for a
@@ -426,7 +416,11 @@ parameter_types! {
 pub type MillauGrandpaInstance = ();
 impl pallet_bridge_grandpa::Config for Runtime {
 	type BridgedChain = bp_millau::Millau;
-	type MaxRequests = MaxRequests;
+	/// This is a pretty unscientific cap.
+	///
+	/// Note that once this is hit the pallet will essentially throttle incoming requests down to
+	/// one call per block.
+	type MaxRequests = ConstU32<50>;
 	type HeadersToKeep = HeadersToKeep;
 	type MaxBridgedAuthorities = MaxAuthoritiesAtMillau;
 	type MaxBridgedHeaderSize = MaxMillauHeaderSize;
diff --git a/bin/rialto/runtime/src/parachains.rs b/bin/rialto/runtime/src/parachains.rs
index 960931a0b3cee..1c7280198a421 100644
--- a/bin/rialto/runtime/src/parachains.rs
+++ b/bin/rialto/runtime/src/parachains.rs
@@ -123,14 +123,10 @@ impl parachains_session_info::Config for Runtime {
 
 impl parachains_shared::Config for Runtime {}
 
-parameter_types! {
-	pub const FirstMessageFactorPercent: u64 = 100;
-}
-
 impl parachains_ump::Config for Runtime {
 	type RuntimeEvent = RuntimeEvent;
 	type UmpSink = ();
-	type FirstMessageFactorPercent = FirstMessageFactorPercent;
+	type FirstMessageFactorPercent = frame_support::traits::ConstU64<100>;
 	type ExecuteOverweightOrigin = EnsureRoot<AccountId>;
 	type WeightInfo = parachains_ump::TestWeightInfo;
 }
diff --git a/bin/rialto/runtime/src/xcm_config.rs b/bin/rialto/runtime/src/xcm_config.rs
index 892c1ed747b19..419a55489307c 100644
--- a/bin/rialto/runtime/src/xcm_config.rs
+++ b/bin/rialto/runtime/src/xcm_config.rs
@@ -27,7 +27,7 @@ use bridge_runtime_common::{
 };
 use frame_support::{
 	parameter_types,
-	traits::{Everything, Nothing},
+	traits::{ConstU32, Everything, Nothing},
 };
 use xcm::latest::prelude::*;
 use xcm_builder::{
@@ -104,10 +104,6 @@ pub type XcmRouter = (
 	XcmBridgeAdapter<ToMillauBridge>,
 );
 
-parameter_types! {
-	pub const MaxAssetsIntoHolding: u32 = 64;
-}
-
 /// The barriers one of which must be passed for an XCM message to be executed.
 pub type Barrier = (
 	// Weight that is paid for may be consumed.
@@ -141,7 +137,7 @@ impl xcm_executor::Config for XcmConfig {
 	type AssetClaims = XcmPallet;
 	type SubscriptionService = XcmPallet;
 	type PalletInstancesInfo = AllPalletsWithSystem;
-	type MaxAssetsIntoHolding = MaxAssetsIntoHolding;
+	type MaxAssetsIntoHolding = ConstU32<64>;
 	type FeeManager = ();
 	type MessageExporter = ();
 	type UniversalAliases = Nothing;
diff --git a/modules/beefy/src/mock.rs b/modules/beefy/src/mock.rs
index 927c39ff9aad4..a07f7962a44d8 100644
--- a/modules/beefy/src/mock.rs
+++ b/modules/beefy/src/mock.rs
@@ -24,7 +24,7 @@ use crate::{
 use bp_beefy::{BeefyValidatorSignatureOf, ChainWithBeefy, Commitment, MmrDataOrHash};
 use bp_runtime::{BasicOperatingMode, Chain};
 use codec::Encode;
-use frame_support::{construct_runtime, parameter_types, weights::Weight};
+use frame_support::{construct_runtime, parameter_types, traits::ConstU64, weights::Weight};
 use sp_core::{sr25519::Signature, Pair};
 use sp_runtime::{
 	testing::{Header, H256},
@@ -72,7 +72,6 @@ construct_runtime! {
 }
 
 parameter_types! {
-	pub const BlockHashCount: u64 = 250;
 	pub const MaximumBlockWeight: Weight = Weight::from_ref_time(1024);
 	pub const MaximumBlockLength: u32 = 2 * 1024;
 	pub const AvailableBlockRatio: Perbill = Perbill::one();
@@ -89,7 +88,7 @@ impl frame_system::Config for TestRuntime {
 	type Lookup = IdentityLookup<Self::AccountId>;
 	type Header = Header;
 	type RuntimeEvent = ();
-	type BlockHashCount = BlockHashCount;
+	type BlockHashCount = ConstU64<250>;
 	type Version = ();
 	type PalletInfo = PalletInfo;
 	type AccountData = ();
diff --git a/modules/grandpa/src/mock.rs b/modules/grandpa/src/mock.rs
index 0f83bd528d68e..12a40a688f6aa 100644
--- a/modules/grandpa/src/mock.rs
+++ b/modules/grandpa/src/mock.rs
@@ -18,7 +18,7 @@
 #![allow(clippy::from_over_into)]
 
 use bp_runtime::Chain;
-use frame_support::{construct_runtime, parameter_types, weights::Weight};
+use frame_support::{construct_runtime, parameter_types, traits::ConstU64, weights::Weight};
 use sp_core::sr25519::Signature;
 use sp_runtime::{
 	testing::{Header, H256},
@@ -50,7 +50,6 @@ construct_runtime! {
 }
 
 parameter_types! {
-	pub const BlockHashCount: u64 = 250;
 	pub const MaximumBlockWeight: Weight = Weight::from_ref_time(1024);
 	pub const MaximumBlockLength: u32 = 2 * 1024;
 	pub const AvailableBlockRatio: Perbill = Perbill::one();
@@ -67,7 +66,7 @@ impl frame_system::Config for TestRuntime {
 	type Lookup = IdentityLookup<Self::AccountId>;
 	type Header = Header;
 	type RuntimeEvent = ();
-	type BlockHashCount = BlockHashCount;
+	type BlockHashCount = ConstU64<250>;
 	type Version = ();
 	type PalletInfo = PalletInfo;
 	type AccountData = ();
diff --git a/modules/messages/src/mock.rs b/modules/messages/src/mock.rs
index 36c38677e5373..da2d1c6a4da4e 100644
--- a/modules/messages/src/mock.rs
+++ b/modules/messages/src/mock.rs
@@ -32,6 +32,7 @@ use bp_runtime::{messages::MessageDispatchResult, Size};
 use codec::{Decode, Encode};
 use frame_support::{
 	parameter_types,
+	traits::ConstU64,
 	weights::{RuntimeDbWeight, Weight},
 };
 use scale_info::TypeInfo;
@@ -104,7 +105,7 @@ impl frame_system::Config for TestRuntime {
 	type Lookup = IdentityLookup<Self::AccountId>;
 	type Header = SubstrateHeader;
 	type RuntimeEvent = RuntimeEvent;
-	type BlockHashCount = BlockHashCount;
+	type BlockHashCount = ConstU64<250>;
 	type Version = ();
 	type PalletInfo = PalletInfo;
 	type AccountData = pallet_balances::AccountData<Balance>;
@@ -120,16 +121,12 @@ impl frame_system::Config for TestRuntime {
 	type MaxConsumers = frame_support::traits::ConstU32<16>;
 }
 
-parameter_types! {
-	pub const ExistentialDeposit: u64 = 1;
-}
-
 impl pallet_balances::Config for TestRuntime {
 	type MaxLocks = ();
 	type Balance = Balance;
 	type DustRemoval = ();
 	type RuntimeEvent = RuntimeEvent;
-	type ExistentialDeposit = ExistentialDeposit;
+	type ExistentialDeposit = ConstU64<1>;
 	type AccountStore = frame_system::Pallet<TestRuntime>;
 	type WeightInfo = ();
 	type MaxReserves = ();
diff --git a/modules/parachains/src/mock.rs b/modules/parachains/src/mock.rs
index 9638472aa985f..4e17a71bcdc5e 100644
--- a/modules/parachains/src/mock.rs
+++ b/modules/parachains/src/mock.rs
@@ -16,7 +16,11 @@
 
 use bp_polkadot_core::parachains::ParaId;
 use bp_runtime::Chain;
-use frame_support::{construct_runtime, parameter_types, traits::IsInVec, weights::Weight};
+use frame_support::{
+	construct_runtime, parameter_types,
+	traits::{ConstU32, IsInVec},
+	weights::Weight,
+};
 use sp_runtime::{
 	testing::{Header, H256},
 	traits::{BlakeTwo256, Header as HeaderT, IdentityLookup},
@@ -86,15 +90,14 @@ impl frame_system::Config for TestRuntime {
 }
 
 parameter_types! {
-	pub const MaxRequests: u32 = 2;
-	pub const HeadersToKeep: u32 = 5;
 	pub const SessionLength: u64 = 5;
 	pub const NumValidators: u32 = 5;
+	pub const HeadersToKeep: u32 = 5;
 }
 
 impl pallet_bridge_grandpa::Config<pallet_bridge_grandpa::Instance1> for TestRuntime {
 	type BridgedChain = TestBridgedChain;
-	type MaxRequests = MaxRequests;
+	type MaxRequests = ConstU32<2>;
 	type HeadersToKeep = HeadersToKeep;
 	type MaxBridgedAuthorities = frame_support::traits::ConstU32<5>;
 	type MaxBridgedHeaderSize = frame_support::traits::ConstU32<512>;
@@ -103,7 +106,7 @@ impl pallet_bridge_grandpa::Config<pallet_bridge_grandpa::Instance1> for TestRun
 
 impl pallet_bridge_grandpa::Config<pallet_bridge_grandpa::Instance2> for TestRuntime {
 	type BridgedChain = TestBridgedChain;
-	type MaxRequests = MaxRequests;
+	type MaxRequests = ConstU32<2>;
 	type HeadersToKeep = HeadersToKeep;
 	type MaxBridgedAuthorities = frame_support::traits::ConstU32<5>;
 	type MaxBridgedHeaderSize = frame_support::traits::ConstU32<512>;
diff --git a/modules/shift-session-manager/src/lib.rs b/modules/shift-session-manager/src/lib.rs
index 073013d92d030..dce6005ab549d 100644
--- a/modules/shift-session-manager/src/lib.rs
+++ b/modules/shift-session-manager/src/lib.rs
@@ -152,7 +152,6 @@ mod tests {
 	}
 
 	parameter_types! {
-		pub const BlockHashCount: u64 = 250;
 		pub const MaximumBlockWeight: Weight = Weight::from_ref_time(1024);
 		pub const MaximumBlockLength: u32 = 2 * 1024;
 		pub const AvailableBlockRatio: Perbill = Perbill::one();
@@ -169,7 +168,7 @@ mod tests {
 		type Lookup = IdentityLookup<Self::AccountId>;
 		type Header = Header;
 		type RuntimeEvent = ();
-		type BlockHashCount = BlockHashCount;
+		type BlockHashCount = frame_support::traits::ConstU64<250>;
 		type Version = ();
 		type PalletInfo = PalletInfo;
 		type AccountData = ();