diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 4e8f9a25e..0d330c32b 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -77,6 +77,7 @@
         - [`generate_seed`](#generate_seed)
         - [`get_beacon_proposer_index`](#get_beacon_proposer_index)
         - [`merkle_root`](#merkle_root)
+        - [`verify_merkle_branch`](#verify_merkle_branch)
         - [`get_attestation_participants`](#get_attestation_participants)
         - [`is_power_of_two`](#is_power_of_two)
         - [`int_to_bytes1`, `int_to_bytes2`, ...](#int_to_bytes1-int_to_bytes2-)
@@ -386,7 +387,7 @@ The following data structures are defined as [SimpleSerialize (SSZ)](https://git
 ```python
 {
     # Branch in the deposit tree
-    'branch': ['bytes32'],
+    'proof': ['bytes32'],
     # Index in the deposit tree
     'index': 'uint64',
     # Data
@@ -983,11 +984,19 @@ def generate_seed(state: BeaconState,
 
 ```python
 def get_beacon_proposer_index(state: BeaconState,
-                              slot: Slot) -> ValidatorIndex:
+                              slot: Slot,
+                              registry_change: bool=False) -> ValidatorIndex:
     """
     Return the beacon proposer index for the ``slot``.
     """
-    first_committee, _ = get_crosslink_committees_at_slot(state, slot)[0]
+    epoch = slot_to_epoch(slot)
+    current_epoch = get_current_epoch(state)
+    previous_epoch = get_previous_epoch(state)
+    next_epoch = current_epoch + 1
+
+    assert previous_epoch <= epoch <= next_epoch
+
+    first_committee, _ = get_crosslink_committees_at_slot(state, slot, registry_change)[0]
     return first_committee[slot % len(first_committee)]
 ```
 
@@ -1005,6 +1014,23 @@ def merkle_root(values: List[Bytes32]) -> Bytes32:
     return o[1]
 ```
 
+### `verify_merkle_branch`
+
+```python
+def verify_merkle_branch(leaf: Bytes32, proof: List[Bytes32], depth: int, index: int, root: Bytes32) -> bool:
+    """
+    Verify that the given ``leaf`` is on the merkle branch ``proof``
+    starting with the given ``root``.
+    """
+    value = leaf
+    for i in range(depth):
+        if index // (2**i) % 2:
+            value = hash(proof[i] + value)
+        else:
+            value = hash(value + proof[i])
+    return value == root
+```
+
 ### `get_attestation_participants`
 
 ```python
@@ -1067,7 +1093,7 @@ def get_effective_balance(state: BeaconState, index: ValidatorIndex) -> Gwei:
 ```python
 def get_total_balance(state: BeaconState, validators: List[ValidatorIndex]) -> Gwei:
     """
-    Return the combined effective balance of an array of validators.
+    Return the combined effective balance of an array of ``validators``.
     """
     return sum([get_effective_balance(state, i) for i in validators])
 ```
@@ -1251,6 +1277,31 @@ def process_deposit(state: BeaconState, deposit: Deposit) -> None:
     """
     deposit_input = deposit.deposit_data.deposit_input
 
+    # Should equal 8 bytes for deposit_data.amount +
+    #              8 bytes for deposit_data.timestamp +
+    #              176 bytes for deposit_data.deposit_input
+    # It should match the deposit_data in the eth1.0 deposit contract
+    serialized_deposit_data = serialize(deposit.deposit_data)
+    # Deposits must be processed in order
+    assert deposit.index == state.deposit_index
+    
+    # Verify the Merkle branch
+    merkle_branch_is_valid = verify_merkle_branch(
+        leaf=hash(serialized_deposit_data),
+        proof=deposit.proof,
+        depth=DEPOSIT_CONTRACT_TREE_DEPTH,
+        index=deposit.index,
+        root=state.latest_eth1_data.deposit_root,
+    )
+    assert merkle_branch_is_valid
+        
+    # Increment the next deposit index we are expecting. Note that this
+    # needs to be done here because while the deposit contract will never
+    # create an invalid Merkle branch, it may admit an invalid deposit
+    # object, and we need to be able to skip over it
+    state.deposit_index += 1
+    
+    # Verify the proof of possession
     proof_is_valid = bls_verify(
         pubkey=deposit_input.pubkey,
         message_hash=signed_root(deposit_input, "proof_of_possession"),
@@ -1506,7 +1557,7 @@ def get_genesis_beacon_state(genesis_validator_deposits: List[Deposit],
         # Ethereum 1.0 chain data
         latest_eth1_data=genesis_eth1_data,
         eth1_data_votes=[],
-        deposit_index=len(genesis_validator_deposits)
+        deposit_index=0,
     )
 
     # Process genesis deposits
@@ -1844,35 +1895,7 @@ def process_attestation(state: BeaconState, attestation: Attestation) -> None:
 
 Verify that `len(block.body.deposits) <= MAX_DEPOSITS`.
 
-[TODO: update the call to `verify_merkle_branch` below if it needs to change after we process deposits in order]
-
-For each `deposit` in `block.body.deposits`:
-
-* Let `serialized_deposit_data` be the serialized form of `deposit.deposit_data`. It should be 8 bytes for `deposit_data.amount` followed by 8 bytes for `deposit_data.timestamp` and then the `DepositInput` bytes. That is, it should match `deposit_data` in the [Ethereum 1.0 deposit contract](#ethereum-10-deposit-contract) of which the hash was placed into the Merkle tree.
-* Verify that `deposit.index == state.deposit_index`.
-* Verify that `verify_merkle_branch(hash(serialized_deposit_data), deposit.branch, DEPOSIT_CONTRACT_TREE_DEPTH, deposit.index, state.latest_eth1_data.deposit_root)` is `True`.
-
-```python
-def verify_merkle_branch(leaf: Bytes32, branch: List[Bytes32], depth: int, index: int, root: Bytes32) -> bool:
-    """
-    Verify that the given ``leaf`` is on the merkle branch ``branch``.
-    """
-    value = leaf
-    for i in range(depth):
-        if index // (2**i) % 2:
-            value = hash(branch[i] + value)
-        else:
-            value = hash(value + branch[i])
-    return value == root
-```
-
-* Run the following:
-
-```python
-process_deposit(state, deposit)
-```
-
-* Set `state.deposit_index += 1`.
+For each `deposit` in `block.body.deposits`, run `process_deposit(state, deposit)`.
 
 ##### Voluntary exits
 
diff --git a/specs/validator/0_beacon-chain-validator.md b/specs/validator/0_beacon-chain-validator.md
index 1523fa507..e1083c5c5 100644
--- a/specs/validator/0_beacon-chain-validator.md
+++ b/specs/validator/0_beacon-chain-validator.md
@@ -50,7 +50,7 @@ __NOTICE__: This document is a work-in-progress for researchers and implementers
                 - [Aggregation bitfield](#aggregation-bitfield)
                 - [Custody bitfield](#custody-bitfield)
                 - [Aggregate signature](#aggregate-signature)
-    - [Validator assigments](#validator-assignments)
+    - [Validator assignments](#validator-assignments)
         - [Lookahead](#lookahead)
     - [How to avoid slashing](#how-to-avoid-slashing)
         - [Proposer slashing](#proposer-slashing)
@@ -371,8 +371,7 @@ def get_committee_assignment(
         if len(selected_committees) > 0:
             validators = selected_committees[0][0]
             shard = selected_committees[0][1]
-            first_committee_at_slot = crosslink_committees[0][0]  # List[ValidatorIndex]
-            is_proposer = first_committee_at_slot[slot % len(first_committee_at_slot)] == validator_index
+            is_proposer = validator_index == get_beacon_proposer_index(state, slot, registry_change=registry_change)
 
             assignment = (validators, shard, slot, is_proposer)
             return assignment