diff --git a/tests/core/pyspec/eth2spec/test/helpers/deposits.py b/tests/core/pyspec/eth2spec/test/helpers/deposits.py
index 565f4bb53..9f7d96981 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/deposits.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/deposits.py
@@ -66,16 +66,16 @@ def deposit_from_context(spec, deposit_data_list, index):
 
 def prepare_full_genesis_deposits(spec,
                                   amount,
-                                  pubkey_max_range,
-                                  pubkey_min_range=0,
+                                  deposit_count,
+                                  min_pubkey_index=0,
                                   signed=False,
                                   deposit_data_list=None):
     if deposit_data_list is None:
         deposit_data_list = []
     genesis_deposits = []
-    for validator_index in range(pubkey_min_range, pubkey_max_range):
-        pubkey = pubkeys[validator_index]
-        privkey = privkeys[validator_index]
+    for pubkey_index in range(min_pubkey_index, min_pubkey_index + deposit_count):
+        pubkey = pubkeys[pubkey_index]
+        privkey = privkeys[pubkey_index]
         # insecurely use pubkey as withdrawal key if no credentials provided
         withdrawal_credentials = spec.BLS_WITHDRAWAL_PREFIX + spec.hash(pubkey)[1:]
         deposit, root, deposit_data_list = build_deposit(
@@ -93,7 +93,7 @@ def prepare_full_genesis_deposits(spec,
 
 
 def prepare_random_genesis_deposits(spec,
-                                    num_deposits,
+                                    deposit_count,
                                     max_pubkey_index,
                                     min_pubkey_index=0,
                                     max_amount=None,
@@ -107,7 +107,7 @@ def prepare_random_genesis_deposits(spec,
     if deposit_data_list is None:
         deposit_data_list = []
     deposits = []
-    for _ in range(num_deposits):
+    for _ in range(deposit_count):
         pubkey_index = rng.randint(min_pubkey_index, max_pubkey_index)
         pubkey = pubkeys[pubkey_index]
         privkey = privkeys[pubkey_index]
diff --git a/tests/core/pyspec/eth2spec/test/phase0/genesis/test_initialization.py b/tests/core/pyspec/eth2spec/test/phase0/genesis/test_initialization.py
index 73ee5528f..b39f5ecfd 100644
--- a/tests/core/pyspec/eth2spec/test/phase0/genesis/test_initialization.py
+++ b/tests/core/pyspec/eth2spec/test/phase0/genesis/test_initialization.py
@@ -45,13 +45,13 @@ def test_initialize_beacon_state_some_small_balances(spec):
     main_deposit_count = spec.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT
     main_deposits, _, deposit_data_list = prepare_full_genesis_deposits(
         spec, spec.MAX_EFFECTIVE_BALANCE,
-        pubkey_max_range=main_deposit_count, signed=True,
+        deposit_count=main_deposit_count, signed=True,
     )
     # For deposits above, and for another deposit_count, add a balance of EFFECTIVE_BALANCE_INCREMENT
     small_deposit_count = main_deposit_count * 2
     small_deposits, deposit_root, _ = prepare_full_genesis_deposits(
         spec, spec.MIN_DEPOSIT_AMOUNT,
-        pubkey_max_range=small_deposit_count,
+        deposit_count=small_deposit_count,
         signed=True,
         deposit_data_list=deposit_data_list,
     )
@@ -83,32 +83,32 @@ def test_initialize_beacon_state_some_small_balances(spec):
 @spec_test
 @single_phase
 def test_initialize_beacon_state_one_topup_activation(spec):
-    # submit all but one deposit as MAX_EFFECTIVE_BALANCE
+    # Submit all but one deposit as MAX_EFFECTIVE_BALANCE
     main_deposit_count = spec.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT - 1
     main_deposits, _, deposit_data_list = prepare_full_genesis_deposits(
         spec, spec.MAX_EFFECTIVE_BALANCE,
-        pubkey_max_range=main_deposit_count, signed=True,
+        deposit_count=main_deposit_count, signed=True,
     )
 
-    # submit last pubkey deposit as MAX_EFFECTIVE_BALANCE - MIN_DEPOSIT_AMOUNT
+    # Submit last pubkey deposit as MAX_EFFECTIVE_BALANCE - MIN_DEPOSIT_AMOUNT
     partial_deposits, _, deposit_data_list = prepare_full_genesis_deposits(
         spec, spec.MAX_EFFECTIVE_BALANCE - spec.MIN_DEPOSIT_AMOUNT,
-        pubkey_max_range=main_deposit_count + 1,
-        pubkey_min_range=main_deposit_count,
+        deposit_count=1,
+        min_pubkey_index=main_deposit_count,
         signed=True,
         deposit_data_list=deposit_data_list,
     )
 
-    # submit last pubkey deposit as MIN_DEPOSIT_AMOUNT to complete the deposit
-    completed_deposits, deposit_root, deposit_data_list = prepare_full_genesis_deposits(
+    # Top up thelast pubkey deposit as MIN_DEPOSIT_AMOUNT to complete the deposit
+    top_up_deposits, _, _ = prepare_full_genesis_deposits(
         spec, spec.MIN_DEPOSIT_AMOUNT,
-        pubkey_max_range=main_deposit_count + 1,
-        pubkey_min_range=main_deposit_count,
+        deposit_count=1,
+        min_pubkey_index=main_deposit_count,
         signed=True,
         deposit_data_list=deposit_data_list,
     )
 
-    deposits = main_deposits + partial_deposits + completed_deposits
+    deposits = main_deposits + partial_deposits + top_up_deposits
 
     eth1_block_hash = b'\x13' * 32
     eth1_timestamp = spec.MIN_GENESIS_TIME
@@ -132,7 +132,7 @@ def test_initialize_beacon_state_random_invalid_genesis(spec):
     # Make a bunch of random deposits
     deposits, _, deposit_data_list = prepare_random_genesis_deposits(
         spec,
-        num_deposits=20,
+        deposit_count=20,
         max_pubkey_index=10,
     )
     eth1_block_hash = b'\x14' * 32
@@ -156,7 +156,7 @@ def test_initialize_beacon_state_random_valid_genesis(spec):
     # Make a bunch of random deposits
     random_deposits, _, deposit_data_list = prepare_random_genesis_deposits(
         spec,
-        num_deposits=20,
+        deposit_count=20,
         min_pubkey_index=spec.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT - 5,
         max_pubkey_index=spec.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT + 5,
     )
@@ -165,7 +165,7 @@ def test_initialize_beacon_state_random_valid_genesis(spec):
     full_deposits, _, _ = prepare_full_genesis_deposits(
         spec,
         spec.MAX_EFFECTIVE_BALANCE,
-        pubkey_max_range=spec.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT,
+        deposit_count=spec.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT,
         signed=True,
         deposit_data_list=deposit_data_list
     )
diff --git a/tests/core/pyspec/eth2spec/test/phase0/genesis/test_validity.py b/tests/core/pyspec/eth2spec/test/phase0/genesis/test_validity.py
index 486f65076..7bdfe1a42 100644
--- a/tests/core/pyspec/eth2spec/test/phase0/genesis/test_validity.py
+++ b/tests/core/pyspec/eth2spec/test/phase0/genesis/test_validity.py
@@ -9,7 +9,7 @@ def create_valid_beacon_state(spec):
     deposits, _, _ = prepare_full_genesis_deposits(
         spec,
         amount=spec.MAX_EFFECTIVE_BALANCE,
-        pubkey_max_range=deposit_count,
+        deposit_count=deposit_count,
         signed=True,
     )
 
@@ -77,7 +77,7 @@ def test_is_valid_genesis_state_true_one_more_validator(spec):
     deposits, _, _ = prepare_full_genesis_deposits(
         spec,
         amount=spec.MAX_EFFECTIVE_BALANCE,
-        pubkey_max_range=deposit_count,
+        deposit_count=deposit_count,
         signed=True,
     )
 
@@ -96,7 +96,7 @@ def test_is_valid_genesis_state_false_not_enough_validator(spec):
     deposits, _, _ = prepare_full_genesis_deposits(
         spec,
         amount=spec.MAX_EFFECTIVE_BALANCE,
-        pubkey_max_range=deposit_count,
+        deposit_count=deposit_count,
         signed=True,
     )