diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 9a680dc7d..4a62342ed 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -1113,6 +1113,9 @@ def initialize_beacon_state_from_eth1(eth1_block_hash: Hash,
         eth1_data=Eth1Data(block_hash=eth1_block_hash, deposit_count=len(deposits)),
         latest_block_header=BeaconBlockHeader(body_root=hash_tree_root(BeaconBlockBody())),
     )
+    # 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 9e3c77b7b..6a9b8f9f1 100644
--- a/test_libs/pyspec/eth2spec/test/helpers/genesis.py
+++ b/test_libs/pyspec/eth2spec/test/helpers/genesis.py
@@ -19,17 +19,23 @@ def build_mock_validator(spec, i: int, balance: int):
 def create_genesis_state(spec, num_validators):
     deposit_root = b'\x42' * 32
 
+    eth1_block_hash = b'\xda' * 32
     state = spec.BeaconState(
         genesis_time=0,
         eth1_deposit_index=num_validators,
         eth1_data=spec.Eth1Data(
             deposit_root=deposit_root,
             deposit_count=num_validators,
-            block_hash=spec.Hash(),
+            block_hash=eth1_block_hash,
         ),
         latest_block_header=spec.BeaconBlockHeader(body_root=spec.hash_tree_root(spec.BeaconBlockBody())),
     )
 
+    # 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