diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 4a62342ed..10640badc 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -1112,10 +1112,8 @@ def initialize_beacon_state_from_eth1(eth1_block_hash: Hash,
         genesis_time=eth1_timestamp - eth1_timestamp % SECONDS_PER_DAY + 2 * SECONDS_PER_DAY,
         eth1_data=Eth1Data(block_hash=eth1_block_hash, deposit_count=len(deposits)),
         latest_block_header=BeaconBlockHeader(body_root=hash_tree_root(BeaconBlockBody())),
+        randao_mixes=[eth1_block_hash] * EPOCHS_PER_HISTORICAL_VECTOR,  # to limit deposit order bias in early epochs
     )
-    # Set the initial RANDAO mixes to hashes seeded by the Eth1 hash, to limit deposit ordering committee bias.
-    for i in range(MIN_SEED_LOOKAHEAD + 1):
-        state.randao_mixes[EPOCHS_PER_HISTORICAL_VECTOR - i - 1] = hash(eth1_block_hash + int_to_bytes(i, 8))
 
     # Process deposits
     leaves = list(map(lambda deposit: deposit.data, deposits))
diff --git a/test_libs/pyspec/eth2spec/test/helpers/genesis.py b/test_libs/pyspec/eth2spec/test/helpers/genesis.py
index 6a9b8f9f1..7e747e34e 100644
--- a/test_libs/pyspec/eth2spec/test/helpers/genesis.py
+++ b/test_libs/pyspec/eth2spec/test/helpers/genesis.py
@@ -29,13 +29,9 @@ def create_genesis_state(spec, num_validators):
             block_hash=eth1_block_hash,
         ),
         latest_block_header=spec.BeaconBlockHeader(body_root=spec.hash_tree_root(spec.BeaconBlockBody())),
+        randao_mixes=[eth1_block_hash] * spec.EPOCHS_PER_HISTORICAL_VECTOR,
     )
 
-    # Set the initial RANDAO mixes to hashes seeded by the Eth1 hash, to limit deposit ordering committee bias.
-    for i in range(spec.MIN_SEED_LOOKAHEAD + 1):
-        state.randao_mixes[spec.EPOCHS_PER_HISTORICAL_VECTOR - i - 1] = \
-            spec.hash(eth1_block_hash + spec.int_to_bytes(i, 8))
-
     # We "hack" in the initial validators,
     #  as it is much faster than creating and processing genesis deposits for every single test case.
     state.balances = [spec.MAX_EFFECTIVE_BALANCE] * num_validators