diff --git a/EIPS/eip-000.md b/EIPS/eip-000.md
index c387ec6793a1dd..d481145d31e46f 100644
--- a/EIPS/eip-000.md
+++ b/EIPS/eip-000.md
@@ -149,6 +149,16 @@ transactions using one, it is reasonable for the protocol to only burn the gas c
 As all transactions in the same block pay exactly the same `baseFeePerGas`, the single cost of accessing a cold item is
 divided evenly among all transactions containing such access and the rest of the burned base fee is refunded.
 
+### Setting an absolute minimal cost of cold state access
+
+If a large number of transactions all access the same addresses or slots, the cost of each cold access may get
+way too low which may represent a potential DoS attack vector.
+
+In order to prevent that, the gas cost of including an entity in the access list cannot be lower
+than `MIN_ACCESS_LIST_ENTRY_COST`, which is set to `32 gas`.
+
+This value is equivalent to the calldata cost of including two bytes long identifier of entries in `block_access_list`.
+
 ### Calculating a refund of the charged priority fee
 
 Each transaction pays an individual `priorityFeePerGas` value and redistributing this part of the cold access cost
@@ -171,6 +181,35 @@ The most expensive transaction contributes a different value because it determin
 A single transaction accessing an address or a slot that is not shared by other transactions does not trigger a refund,
 and therefore has a zero marginal contribution.
 
+### Efficiently storing the access lists in the block history
+
+The contents of the `accessList` parameter are part of the Ethereum history and the potential cost of keeping this
+data in the blockchain must be accounted for when implementing this change.
+There is currently no additional charge applied to the `accessList` parameter, due to the cost of including
+an address or a storage slot in the `accessList` being a constant value that is significantly higher than the
+potential cost of storing the `accessList` at the cost of  a
+dynamically sized `calldata` field.
+
+With the block-level warming there is a change that makes it possible for a transaction sender to construct
+transactions with a large `accessList` that cost very little to be included, and this can be used to bloat the
+blockchain size.
+
+This potential bloating of the block size also presents a challenge for the propagation of the block in a P2P network.
+
+In order to minimize the cost of permanently storing access lists, we propose the following changes to
+the `execution_payload` structure:
+
+1. Add a new `block_access_list` field. \
+ The execution clients create a combined block-level "access list" that contains all unique entries from all
+ transactions in the block.
+2. All individual transaction `accessList` fields replace the full entries with a
+ compact 2 bytes long reference to the `block_access_list` in the same order they appeared originally.
+
+With this approach shared entries in the access lists cannot cause sufficient bloating of the block size.
+
+There is no need to introduce any observable changes to the RPC API as this "compression" can be unwrapped by the
+clients in real time.
+
 ### Pseudocode implementation of the refund calculation algorithm
 
 ```typescript
@@ -201,7 +240,8 @@ function calculateItemColdAccessRefund (
   for (let i = 0; i < sortedAccessDetails.length; i++) {
     const accessor = sortedAccessDetails[i]
     const refund = refunds.get(accessor.sender) ?? { refundFromBurn: 0n, refundFromCoinbase: 0n }
-    refund.refundFromBurn += BigInt(Math.floor(parseInt(accessGasCost) * parseInt(baseFeePerGas) * refundPercent))
+    const adjustedAccessGasCost = Math.max(MIN_ACCESS_LIST_ENTRY_COST, parseInt(accessGasCost) * refundPercent)
+    refund.refundFromBurn += BigInt(adjustedAccessGasCost * parseInt(baseFeePerGas))
     refund.refundFromCoinbase += BigInt(refundsFromCoinbase[i])
     refunds.set(accessor.sender, refund)
   }
@@ -234,7 +274,10 @@ export function calculatePriorityFeeRefunds (sortedAccesses: AccessDetails[], ac
   const refunds = [Math.floor(totalRefund * topTransactionContribution / totalContributions)]
   for (let i = 1; i < sortedAccesses.length; i++) {
     const charge = parseInt(sortedAccesses[i].priorityFeePerGas) * parseInt(accessGasCost)
-    refunds.push(Math.floor(totalRefund * charge / totalContributions))
+    const calldataCharge = parseInt(sortedAccesses[i].priorityFeePerGas) * MIN_ACCESS_LIST_ENTRY_COST
+    const refundToCalldata = charge - calldataCharge
+    const refundToContribution = Math.floor(totalRefund * charge / totalContributions)
+    refunds.push(Math.min(refundToCalldata, refundToContribution))
   }
   return refunds
 }