diff --git a/bridges/primitives/chain-bridge-hub-cumulus/src/lib.rs b/bridges/primitives/chain-bridge-hub-cumulus/src/lib.rs
index ecf263d4a09c67f40cff0a3fbca9623e63b80e27..0f5f33087edc731de8eb22a3cfc36ea795910afd 100644
--- a/bridges/primitives/chain-bridge-hub-cumulus/src/lib.rs
+++ b/bridges/primitives/chain-bridge-hub-cumulus/src/lib.rs
@@ -20,8 +20,7 @@ use bp_messages::*;
 pub use bp_polkadot_core::{
 	AccountId, AccountInfoStorageMapKeyProvider, AccountPublic, Balance, BlockNumber, Hash, Hasher,
 	Hashing, Header, Index, Nonce, Perbill, Signature, SignedBlock, SignedExtensions,
-	UncheckedExtrinsic, MAX_UNCONFIRMED_MESSAGES_IN_CONFIRMATION_TX,
-	MAX_UNREWARDED_RELAYERS_IN_CONFIRMATION_TX, TX_EXTRA_BYTES,
+	UncheckedExtrinsic, TX_EXTRA_BYTES,
 };
 use frame_support::{
 	dispatch::DispatchClass,
@@ -85,3 +84,32 @@ pub type AccountSigner = MultiSigner;
 
 /// The address format for describing accounts.
 pub type Address = MultiAddress<AccountId, ()>;
+
+// Note about selecting values of two following constants:
+//
+// Normal transactions have limit of 75% of 1/2 second weight for Cumulus parachains. Let's keep
+// some reserve for the rest of stuff there => let's select values that fit in 50% of maximal limit.
+//
+// Using current constants, the limit would be:
+//
+// `75% * WEIGHT_REF_TIME_PER_SECOND * 1 / 2 * 50% = 0.75 * 1_000_000_000_000 / 2 * 0.5 =
+// 187_500_000_000`
+//
+// According to (preliminary) weights of messages pallet, cost of additional message is zero and the
+// cost of additional relayer is `8_000_000 + db read + db write`. Let's say we want no more than
+// 4096 unconfirmed messages (no any scientific justification for that - it just looks large
+// enough). And then we can't have more than 4096 relayers. E.g. for 1024 relayers is (using
+// `RocksDbWeight`):
+//
+// `1024 * (8_000_000 + db read + db write) = 1024 * (8_000_000 + 25_000_000 + 100_000_000) =
+// 136_192_000_000`
+//
+// So 1024 looks like good approximation for the number of relayers. If something is wrong in those
+// assumptions, or something will change, it shall be caught by the
+// `ensure_able_to_receive_confirmation` test.
+
+/// Maximal number of unrewarded relayer entries at inbound lane for Cumulus-based parachains.
+pub const MAX_UNREWARDED_RELAYERS_IN_CONFIRMATION_TX: MessageNonce = 1024;
+
+/// Maximal number of unconfirmed messages at inbound lane for Cumulus-based parachains.
+pub const MAX_UNCONFIRMED_MESSAGES_IN_CONFIRMATION_TX: MessageNonce = 4096;
diff --git a/bridges/primitives/polkadot-core/src/lib.rs b/bridges/primitives/polkadot-core/src/lib.rs
index 57025f2f3f697726cef37abfc3c5d9a3a11c3b8c..8d9932ea58c52c44d064d35dbdb7b545afe9bb76 100644
--- a/bridges/primitives/polkadot-core/src/lib.rs
+++ b/bridges/primitives/polkadot-core/src/lib.rs
@@ -118,14 +118,6 @@ parameter_types! {
 /// Maximal number of messages in single delivery transaction.
 pub const MAX_MESSAGES_IN_DELIVERY_TRANSACTION: MessageNonce = 128;
 
-/// Maximal number of unrewarded relayer entries at inbound lane.
-pub const MAX_UNREWARDED_RELAYERS_IN_CONFIRMATION_TX: MessageNonce = 128;
-
-// TODO [#438] should be selected keeping in mind:
-// finality delay on both chains + reward payout cost + messages throughput.
-/// Maximal number of unconfirmed messages at inbound lane.
-pub const MAX_UNCONFIRMED_MESSAGES_IN_CONFIRMATION_TX: MessageNonce = 8192;
-
 /// Maximal number of bytes, included in the signed Polkadot-like transaction apart from the encoded
 /// call itself.
 ///