diff --git a/tests/core/pyspec/eth2spec/test/fork_choice/test_on_attestation.py b/tests/core/pyspec/eth2spec/test/fork_choice/test_on_attestation.py
index 09248944c..87a39a620 100644
--- a/tests/core/pyspec/eth2spec/test/fork_choice/test_on_attestation.py
+++ b/tests/core/pyspec/eth2spec/test/fork_choice/test_on_attestation.py
@@ -1,7 +1,7 @@
 from eth2spec.test.context import with_all_phases, spec_state_test
 from eth2spec.test.helpers.block import build_empty_block_for_next_slot
 from eth2spec.test.helpers.attestations import get_valid_attestation, sign_attestation
-from eth2spec.test.helpers.state import transition_to, state_transition_and_sign_block
+from eth2spec.test.helpers.state import transition_to, state_transition_and_sign_block, next_epoch
 
 
 def run_on_attestation(spec, state, store, attestation, valid=True):
@@ -179,7 +179,7 @@ def test_on_attestation_future_epoch(spec, state):
     spec.on_block(store, signed_block)
 
     # move state forward but not store
-    state.slot = block.slot + spec.SLOTS_PER_EPOCH
+    next_epoch(spec, state)
 
     attestation = get_valid_attestation(spec, state, slot=state.slot, signed=True)
     run_on_attestation(spec, state, store, attestation, False)
diff --git a/tests/core/pyspec/eth2spec/test/helpers/state.py b/tests/core/pyspec/eth2spec/test/helpers/state.py
index aad329ff4..5816785f7 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/state.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/state.py
@@ -14,6 +14,13 @@ def next_slot(spec, state):
     spec.process_slots(state, state.slot + 1)
 
 
+def next_slots(spec, state, slots):
+    """
+    Transition given slots forward.
+    """
+    spec.process_slots(state, state.slot + slots)
+
+
 def transition_to(spec, state, slot):
     """
     Transition to ``slot``.
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py b/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py
index 64a64c72d..1dbdafec2 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py
@@ -13,7 +13,7 @@ from eth2spec.test.helpers.attestations import (
     sign_attestation,
 )
 from eth2spec.test.helpers.state import (
-    next_epoch,
+    next_epoch, next_slots
 )
 from eth2spec.test.helpers.block import apply_empty_block
 from eth2spec.utils.ssz.ssz_typing import Bitlist
@@ -58,7 +58,7 @@ def run_attestation_processing(spec, state, attestation, valid=True):
 @spec_state_test
 def test_success(spec, state):
     attestation = get_valid_attestation(spec, state, signed=True)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     yield from run_attestation_processing(spec, state, attestation)
 
@@ -68,9 +68,9 @@ def test_success(spec, state):
 @with_custom_state(balances_fn=low_balances, threshold_fn=lambda spec: spec.EJECTION_BALANCE)
 @single_phase
 def test_success_multi_proposer_index_iterations(spec, state):
-    state.slot += spec.SLOTS_PER_EPOCH * 2
+    next_slots(spec, state, spec.SLOTS_PER_EPOCH * 2)
     attestation = get_valid_attestation(spec, state, signed=True)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     yield from run_attestation_processing(spec, state, attestation)
 
@@ -91,7 +91,7 @@ def test_success_previous_epoch(spec, state):
 @always_bls
 def test_invalid_attestation_signature(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     yield from run_attestation_processing(spec, state, attestation, False)
 
@@ -120,7 +120,7 @@ def test_after_epoch_slots(spec, state):
 @with_all_phases
 @spec_state_test
 def test_old_source_epoch(spec, state):
-    state.slot = spec.SLOTS_PER_EPOCH * 5
+    next_slots(spec, state, spec.SLOTS_PER_EPOCH * 5)
     state.finalized_checkpoint.epoch = 2
     state.previous_justified_checkpoint.epoch = 3
     state.current_justified_checkpoint.epoch = 4
@@ -142,7 +142,7 @@ def test_old_source_epoch(spec, state):
 @always_bls
 def test_wrong_index_for_committee_signature(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     attestation.data.index += 1
 
@@ -160,7 +160,7 @@ def test_wrong_index_for_slot(spec, state):
     index = spec.MAX_COMMITTEES_PER_SLOT - 1
 
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     attestation.data.index = index
 
@@ -172,7 +172,7 @@ def test_wrong_index_for_slot(spec, state):
 @never_bls
 def test_invalid_index(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     # off by one (with respect to valid range) on purpose
     attestation.data.index = spec.MAX_COMMITTEES_PER_SLOT
@@ -223,7 +223,7 @@ def test_future_target_epoch(spec, state):
     # manually add signature for correct participants
     attestation.signature = sign_aggregate_attestation(spec, state, attestation.data, participants)
 
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     yield from run_attestation_processing(spec, state, attestation, False)
 
@@ -232,7 +232,7 @@ def test_future_target_epoch(spec, state):
 @spec_state_test
 def test_new_source_epoch(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     attestation.data.source.epoch += 1
 
@@ -245,7 +245,7 @@ def test_new_source_epoch(spec, state):
 @spec_state_test
 def test_source_root_is_target_root(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     attestation.data.source.root = attestation.data.target.root
 
@@ -264,7 +264,7 @@ def test_invalid_current_source_root(spec, state):
     state.current_justified_checkpoint = spec.Checkpoint(epoch=4, root=b'\x32' * 32)
 
     attestation = get_valid_attestation(spec, state, slot=(spec.SLOTS_PER_EPOCH * 3) + 1)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     # Test logic sanity checks:
     assert state.current_justified_checkpoint.root != state.previous_justified_checkpoint.root
@@ -282,7 +282,7 @@ def test_invalid_current_source_root(spec, state):
 @spec_state_test
 def test_bad_source_root(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     attestation.data.source.root = b'\x42' * 32
 
@@ -295,7 +295,7 @@ def test_bad_source_root(spec, state):
 @spec_state_test
 def test_empty_aggregation_bits(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     attestation.aggregation_bits = Bitlist[spec.MAX_VALIDATORS_PER_COMMITTEE](
         *([0b0] * len(attestation.aggregation_bits)))
@@ -309,7 +309,7 @@ def test_empty_aggregation_bits(spec, state):
 @spec_state_test
 def test_too_many_aggregation_bits(spec, state):
     attestation = get_valid_attestation(spec, state, signed=True)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     # one too many bits
     attestation.aggregation_bits.append(0b0)
@@ -321,7 +321,7 @@ def test_too_many_aggregation_bits(spec, state):
 @spec_state_test
 def test_too_few_aggregation_bits(spec, state):
     attestation = get_valid_attestation(spec, state)
-    state.slot += spec.MIN_ATTESTATION_INCLUSION_DELAY
+    next_slots(spec, state, spec.MIN_ATTESTATION_INCLUSION_DELAY)
 
     attestation.aggregation_bits = Bitlist[spec.MAX_VALIDATORS_PER_COMMITTEE](
         *([0b1] + [0b0] * (len(attestation.aggregation_bits) - 1)))
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_proposer_slashing.py b/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_proposer_slashing.py
index 30b3c1fdd..ad910f227 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_proposer_slashing.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/block_processing/test_process_proposer_slashing.py
@@ -2,7 +2,7 @@ from eth2spec.test.context import spec_state_test, expect_assertion_error, alway
 from eth2spec.test.helpers.block_header import sign_block_header
 from eth2spec.test.helpers.keys import privkeys
 from eth2spec.test.helpers.proposer_slashings import get_valid_proposer_slashing
-from eth2spec.test.helpers.state import get_balance
+from eth2spec.test.helpers.state import get_balance, next_epoch
 
 
 def run_proposer_slashing_processing(spec, state, proposer_slashing, valid=True):
@@ -135,7 +135,7 @@ def test_proposer_is_withdrawn(spec, state):
     proposer_slashing = get_valid_proposer_slashing(spec, state, signed_1=True, signed_2=True)
 
     # move 1 epoch into future, to allow for past withdrawable epoch
-    state.slot += spec.SLOTS_PER_EPOCH
+    next_epoch(spec, state)
     # set proposer withdrawable_epoch in past
     current_epoch = spec.get_current_epoch(state)
     proposer_index = proposer_slashing.proposer_index
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_final_updates.py b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_final_updates.py
index 58882a44f..2e71346aa 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_final_updates.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_final_updates.py
@@ -2,6 +2,7 @@ from eth2spec.test.context import spec_state_test, with_all_phases
 from eth2spec.test.phase_0.epoch_processing.run_epoch_process_base import (
     run_epoch_processing_with, run_epoch_processing_to
 )
+from eth2spec.test.helpers.state import transition_to
 
 
 def run_process_final_updates(spec, state):
@@ -13,7 +14,8 @@ def run_process_final_updates(spec, state):
 def test_eth1_vote_no_reset(spec, state):
     assert spec.SLOTS_PER_ETH1_VOTING_PERIOD > spec.SLOTS_PER_EPOCH
     # skip ahead to the end of the epoch
-    state.slot = spec.SLOTS_PER_EPOCH - 1
+    transition_to(spec, state, spec.SLOTS_PER_EPOCH - 1)
+
     for i in range(state.slot + 1):  # add a vote for each skipped slot.
         state.eth1_data_votes.append(
             spec.Eth1Data(deposit_root=b'\xaa' * 32,
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py
index 6fc4e30cb..9f9e1c316 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_justification_and_finalization.py
@@ -2,6 +2,7 @@ from eth2spec.test.context import spec_state_test, with_all_phases
 from eth2spec.test.phase_0.epoch_processing.run_epoch_process_base import (
     run_epoch_processing_with
 )
+from eth2spec.test.helpers.state import transition_to
 
 
 def run_process_just_and_fin(spec, state):
@@ -82,7 +83,7 @@ def put_checkpoints_in_block_roots(spec, state, checkpoints):
 
 def finalize_on_234(spec, state, epoch, sufficient_support):
     assert epoch > 4
-    state.slot = (spec.SLOTS_PER_EPOCH * epoch) - 1  # skip ahead to just before epoch
+    transition_to(spec, state, spec.SLOTS_PER_EPOCH * epoch - 1)  # skip ahead to just before epoch
 
     # 43210 -- epochs ago
     # 3210x -- justification bitfield indices
@@ -117,7 +118,7 @@ def finalize_on_234(spec, state, epoch, sufficient_support):
 
 def finalize_on_23(spec, state, epoch, sufficient_support):
     assert epoch > 3
-    state.slot = (spec.SLOTS_PER_EPOCH * epoch) - 1  # skip ahead to just before epoch
+    transition_to(spec, state, spec.SLOTS_PER_EPOCH * epoch - 1)  # skip ahead to just before epoch
 
     # 43210 -- epochs ago
     # 210xx  -- justification bitfield indices (pre shift)
@@ -195,7 +196,7 @@ def finalize_on_123(spec, state, epoch, sufficient_support):
 
 def finalize_on_12(spec, state, epoch, sufficient_support, messed_up_target):
     assert epoch > 2
-    state.slot = (spec.SLOTS_PER_EPOCH * epoch) - 1  # skip ahead to just before epoch
+    transition_to(spec, state, spec.SLOTS_PER_EPOCH * epoch - 1)  # skip ahead to just before epoch
 
     # 43210 -- epochs ago
     # 210xx  -- justification bitfield indices (pre shift)
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_registry_updates.py b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_registry_updates.py
index 526aba277..a5f4d9227 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_registry_updates.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_registry_updates.py
@@ -1,4 +1,4 @@
-from eth2spec.test.helpers.state import next_epoch
+from eth2spec.test.helpers.state import next_epoch, next_slots
 from eth2spec.test.context import spec_state_test, with_all_phases
 from eth2spec.test.phase_0.epoch_processing.run_epoch_process_base import run_epoch_processing_with
 
@@ -101,7 +101,7 @@ def test_activation_queue_sorting(spec, state):
     state.validators[mock_activations - 1].activation_eligibility_epoch = epoch
 
     # move state forward and finalize to allow for activations
-    state.slot += spec.SLOTS_PER_EPOCH * 3
+    next_slots(spec, state, spec.SLOTS_PER_EPOCH * 3)
     state.finalized_checkpoint.epoch = epoch + 1
 
     yield from run_process_registry_updates(spec, state)
@@ -113,10 +113,10 @@ def test_activation_queue_sorting(spec, state):
     # the second last is at the end of the queue, and did not make the churn,
     #  hence is not assigned an activation_epoch yet.
     assert state.validators[mock_activations - 2].activation_epoch == spec.FAR_FUTURE_EPOCH
-    # the one at churn_limit - 1 did not make it, it was out-prioritized
-    assert state.validators[churn_limit - 1].activation_epoch == spec.FAR_FUTURE_EPOCH
+    # the one at churn_limit did not make it, it was out-prioritized
+    assert state.validators[churn_limit].activation_epoch == spec.FAR_FUTURE_EPOCH
     # but the the one in front of the above did
-    assert state.validators[churn_limit - 2].activation_epoch != spec.FAR_FUTURE_EPOCH
+    assert state.validators[churn_limit - 1].activation_epoch != spec.FAR_FUTURE_EPOCH
 
 
 @with_all_phases
@@ -131,7 +131,8 @@ def test_activation_queue_efficiency(spec, state):
         state.validators[i].activation_eligibility_epoch = epoch + 1
 
     # move state forward and finalize to allow for activations
-    state.slot += spec.SLOTS_PER_EPOCH * 3
+    next_slots(spec, state, spec.SLOTS_PER_EPOCH * 3)
+
     state.finalized_checkpoint.epoch = epoch + 1
 
     # Run first registry update. Do not yield test vectors
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_slashings.py b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_slashings.py
index c58da5a4a..23c8ce11a 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_slashings.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_slashings.py
@@ -2,6 +2,7 @@ from eth2spec.test.context import spec_state_test, with_all_phases
 from eth2spec.test.phase_0.epoch_processing.run_epoch_process_base import (
     run_epoch_processing_with, run_epoch_processing_to
 )
+from eth2spec.test.helpers.state import next_epoch
 
 
 def run_process_slashings(spec, state):
@@ -79,7 +80,7 @@ def test_small_penalty(spec, state):
 @spec_state_test
 def test_scaled_penalties(spec, state):
     # skip to next epoch
-    state.slot = spec.SLOTS_PER_EPOCH
+    next_epoch(spec, state)
 
     # Also mock some previous slashings, so that we test to have the delta in the penalties computation.
     base = spec.EJECTION_BALANCE
diff --git a/tests/core/pyspec/eth2spec/test/sanity/test_blocks.py b/tests/core/pyspec/eth2spec/test/sanity/test_blocks.py
index 9027660ab..e533b3b0a 100644
--- a/tests/core/pyspec/eth2spec/test/sanity/test_blocks.py
+++ b/tests/core/pyspec/eth2spec/test/sanity/test_blocks.py
@@ -2,7 +2,7 @@ from copy import deepcopy
 
 from eth2spec.utils import bls
 
-from eth2spec.test.helpers.state import get_balance, state_transition_and_sign_block, next_slot
+from eth2spec.test.helpers.state import get_balance, state_transition_and_sign_block, next_slot, next_epoch
 from eth2spec.test.helpers.block import build_empty_block_for_next_slot, build_empty_block, sign_block, \
     transition_unsigned_block
 from eth2spec.test.helpers.keys import privkeys, pubkeys
@@ -11,7 +11,7 @@ from eth2spec.test.helpers.proposer_slashings import get_valid_proposer_slashing
 from eth2spec.test.helpers.attestations import get_valid_attestation
 from eth2spec.test.helpers.deposits import prepare_state_and_deposit
 
-from eth2spec.test.context import spec_state_test, with_all_phases, expect_assertion_error, always_bls
+from eth2spec.test.context import spec_state_test, with_all_phases, expect_assertion_error, always_bls, with_phases
 
 
 @with_all_phases
@@ -260,7 +260,8 @@ def test_proposer_after_inactive_index(spec, state):
     state.validators[inactive_index].exit_epoch = spec.get_current_epoch(state)
 
     # skip forward, get brand new proposers
-    state.slot = spec.SLOTS_PER_EPOCH * 2
+    next_epoch(spec, state)
+    next_epoch(spec, state)
     block = build_empty_block_for_next_slot(spec, state)
     state_transition_and_sign_block(spec, state, block)
 
@@ -372,7 +373,7 @@ def test_deposit_top_up(spec, state):
 @with_all_phases
 @spec_state_test
 def test_attestation(spec, state):
-    state.slot = spec.SLOTS_PER_EPOCH
+    next_epoch(spec, state)
 
     yield 'pre', state
 
@@ -399,7 +400,9 @@ def test_attestation(spec, state):
     assert spec.hash_tree_root(state.previous_epoch_attestations) == pre_current_attestations_root
 
 
-@with_all_phases
+# In phase1 a committee is computed for PERSISTENT_COMMITTEE_PERIOD slots ago,
+# exceeding the minimal-config randao mixes memory size.
+@with_phases(['phase0'])
 @spec_state_test
 def test_voluntary_exit(spec, state):
     validator_index = spec.get_active_validator_indices(