diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 0facc0a85..eeac36683 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -656,54 +656,71 @@ SECONDS_PER_DAY: constant(uint256) = 86400
 Deposit: event({previous_deposit_root: bytes32, data: bytes[2064], merkle_tree_index: bytes[8]})
 ChainStart: event({deposit_root: bytes32, time: bytes[8]})
 
-deposit_tree: map(uint256, bytes32)
+zerohashes: bytes32[32]
+branch: bytes32[32]
 deposit_count: uint256
 full_deposit_count: uint256
 
+@public
+def __init__():
+    for i in range(31):
+        self.zerohashes[i+1] = sha3(concat(self.zerohashes[i], self.zerohashes[i]))
+        self.branch[i+1] = self.zerohashes[i+1]
+
+@public
+@constant
+def get_deposit_root() -> bytes32:
+    root:bytes32 = 0x0000000000000000000000000000000000000000000000000000000000000000
+    size:uint256 = self.deposit_count
+    for h in range(32):
+        if size % 2 == 1:
+            root = sha3(concat(self.branch[h], root))
+        else:
+            root = sha3(concat(root, self.branch[h]))
+        size /= 2
+    return root
+
 @payable
 @public
 def deposit(deposit_input: bytes[2048]):
     assert msg.value >= as_wei_value(MIN_DEPOSIT_AMOUNT, "gwei")
     assert msg.value <= as_wei_value(MAX_DEPOSIT_AMOUNT, "gwei")
 
-    index: uint256 = self.deposit_count + TWO_TO_POWER_OF_TREE_DEPTH
+    index: uint256 = self.deposit_count
     deposit_amount: bytes[8] = slice(concat("", convert(msg.value / GWEI_PER_ETH, bytes32)), start=24, len=8)
     deposit_timestamp: bytes[8] = slice(concat("", convert(block.timestamp, bytes32)), start=24, len=8)
     deposit_data: bytes[2064] = concat(deposit_amount, deposit_timestamp, deposit_input)
     merkle_tree_index: bytes[8] = slice(concat("", convert(index, bytes32)), start=24, len=8)
 
-    log.Deposit(self.deposit_tree[1], deposit_data, merkle_tree_index)
-
     # add deposit to merkle tree
-    self.deposit_tree[index] = sha3(deposit_data)
-    for i in range(DEPOSIT_CONTRACT_TREE_DEPTH):
-        index /= 2
-        self.deposit_tree[index] = sha3(concat(self.deposit_tree[index * 2], self.deposit_tree[index * 2 + 1]))
+    i: int128 = 0
+    power_of_two: uint256 = 2
+    for _ in range(32):
+        if (index+1) % power_of_two != 0:
+            break
+        i += 1
+        power_of_two *= 2
+    value:bytes32 = sha3(deposit_data)
+    for j in range(32):
+        if j < i:
+            value = sha3(concat(self.branch[j], value))
+            self.branch[j] = self.zerohashes[j]
+    self.branch[i] = value
 
     self.deposit_count += 1
+
+    log.Deposit(self.get_deposit_root(), deposit_data, merkle_tree_index)
+
     if msg.value == as_wei_value(MAX_DEPOSIT_AMOUNT, "gwei"):
         self.full_deposit_count += 1
         if self.full_deposit_count == CHAIN_START_FULL_DEPOSIT_THRESHOLD:
             timestamp_day_boundary: uint256 = as_unitless_number(block.timestamp) - as_unitless_number(block.timestamp) % SECONDS_PER_DAY + SECONDS_PER_DAY
             chainstart_time: bytes[8] = slice(concat("", convert(timestamp_day_boundary, bytes32)), start=24, len=8)
-            log.ChainStart(self.deposit_tree[1], chainstart_time)
-
-@public
-@constant
-def get_deposit_root() -> bytes32:
-    return self.deposit_tree[1]
-
-@public
-@constant
-def get_branch(leaf: uint256) -> bytes32[32]: # size is DEPOSIT_CONTRACT_TREE_DEPTH (symbolic const not supported)
-    branch: bytes32[32] # size is DEPOSIT_CONTRACT_TREE_DEPTH
-    index: uint256 = leaf + TWO_TO_POWER_OF_TREE_DEPTH
-    for i in range(DEPOSIT_CONTRACT_TREE_DEPTH):
-        branch[i] = self.deposit_tree[bitwise_xor(index, 1)]
-        index /= 2
-    return branch
+            log.ChainStart(self.get_deposit_root(), chainstart_time)
 ```
 
+Note: to save ~10x on gas this contract uses a somewhat unintuitive progressive Merkle root calculation algo that requires only O(log(n)) storage. See https://github.com/ethereum/research/blob/master/beacon_chain_impl/progressive_merkle_tree.py for an implementation of the same algo in python tested for correctness.
+
 ## Beacon chain processing
 
 The beacon chain is the system chain for Ethereum 2.0. The main responsibilities of the beacon chain are: