diff --git a/specs/core/1_custody-game.md b/specs/core/1_custody-game.md
index 48100e7ba..f79977442 100644
--- a/specs/core/1_custody-game.md
+++ b/specs/core/1_custody-game.md
@@ -15,7 +15,7 @@
         - [Time parameters](#time-parameters)
         - [Max operations per block](#max-operations-per-block)
         - [Reward and penalty quotients](#reward-and-penalty-quotients)
-        - [Signature domains](#signature-domains)
+        - [Signature domain types](#signature-domain-types)
         - [TODO PLACEHOLDER](#todo-placeholder)
     - [Data structures](#data-structures)
         - [Custody objects](#custody-objects)
@@ -156,7 +156,7 @@ class CustodyChunkChallengeRecord(Container):
     challenger_index: ValidatorIndex
     responder_index: ValidatorIndex
     inclusion_epoch: Epoch
-    data_root: Bytes32
+    data_root: Hash
     depth: uint64
     chunk_index: uint64
 ```
@@ -169,9 +169,9 @@ class CustodyBitChallengeRecord(Container):
     challenger_index: ValidatorIndex
     responder_index: ValidatorIndex
     inclusion_epoch: Epoch
-    data_root: Bytes32
+    data_root: Hash
     chunk_count: uint64
-    chunk_bits_merkle_root: Bytes32
+    chunk_bits_merkle_root: Hash
     responder_key: BLSSignature
 ```
 
@@ -182,9 +182,9 @@ class CustodyResponse(Container):
     challenge_index: uint64
     chunk_index: uint64
     chunk: Vector[Bytes[PLACEHOLDER], BYTES_PER_CUSTODY_CHUNK]
-    data_branch: List[Bytes32, PLACEHOLDER]
-    chunk_bits_branch: List[Bytes32, PLACEHOLDER]
-    chunk_bits_leaf: Bytes32
+    data_branch: List[Hash, PLACEHOLDER]
+    chunk_bits_branch: List[Hash, PLACEHOLDER]
+    chunk_bits_leaf: Hash
 ```
 
 ### New beacon operations
@@ -296,7 +296,7 @@ def get_custody_chunk_bit(key: BLSSignature, chunk: bytes) -> bool:
 ### `get_chunk_bits_root`
 
 ```python
-def get_chunk_bits_root(chunk_bits: bytes) -> Bytes32:
+def get_chunk_bits_root(chunk_bits: bytes) -> Hash:
     aggregated_bits = bytearray([0] * 32)
     for i in range(0, len(chunk_bits), 32):
         for j in range(32):
diff --git a/specs/core/1_shard-data-chains.md b/specs/core/1_shard-data-chains.md
index 330840598..fb4f353ef 100644
--- a/specs/core/1_shard-data-chains.md
+++ b/specs/core/1_shard-data-chains.md
@@ -93,7 +93,7 @@ class ShardAttestation(Container):
     class data(Container):
         slot: Slot
         shard: Shard
-        shard_block_root: Bytes32
+        shard_block_root: Hash
     aggregation_bits: Bitlist[PLACEHOLDER]
     aggregate_signature: BLSSignature
 ```
@@ -104,10 +104,10 @@ class ShardAttestation(Container):
 class ShardBlock(Container):
     slot: Slot
     shard: Shard
-    beacon_chain_root: Bytes32
-    parent_root: Bytes32
+    beacon_chain_root: Hash
+    parent_root: Hash
     data: ShardBlockBody
-    state_root: Bytes32
+    state_root: Hash
     attestations: List[ShardAttestation, PLACEHOLDER]
     signature: BLSSignature
 ```
@@ -118,10 +118,10 @@ class ShardBlock(Container):
 class ShardBlockHeader(Container):
     slot: Slot
     shard: Shard
-    beacon_chain_root: Bytes32
-    parent_root: Bytes32
-    body_root: Bytes32
-    state_root: Bytes32
+    beacon_chain_root: Hash
+    parent_root: Hash
+    body_root: Hash
+    state_root: Hash
     attestations: List[ShardAttestation, PLACEHOLDER]
     signature: BLSSignature
 ```
@@ -249,7 +249,7 @@ def verify_shard_attestation_signature(state: BeaconState,
 ### `compute_crosslink_data_root`
 
 ```python
-def compute_crosslink_data_root(blocks: Sequence[ShardBlock]) -> Bytes32:
+def compute_crosslink_data_root(blocks: Sequence[ShardBlock]) -> Hash:
     def is_power_of_two(value: uint64) -> bool:
         return (value > 0) and (value & (value - 1) == 0)
 
@@ -258,7 +258,7 @@ def compute_crosslink_data_root(blocks: Sequence[ShardBlock]) -> Bytes32:
             values.append(b'\x00' * BYTES_PER_SHARD_BLOCK_BODY)
         return values
 
-    def hash_tree_root_of_bytes(data: bytes) -> bytes:
+    def hash_tree_root_of_bytes(data: bytes) -> Hash:
         return hash_tree_root([data[i:i + 32] for i in range(0, len(data), 32)])
 
     def zpad(data: bytes, length: uint64) -> bytes: