diff --git a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py
index d48386fd4..7937614a4 100644
--- a/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py
+++ b/test_libs/pyspec/eth2spec/test/phase_0/block_processing/test_process_attestation.py
@@ -6,7 +6,7 @@ from eth2spec.test.context import (
     spec_test,
     low_balances,
     with_custom_state,
-)
+    single_phase)
 from eth2spec.test.helpers.attestations import (
     get_valid_attestation,
     sign_aggregate_attestation,
@@ -66,6 +66,7 @@ def test_success(spec, state):
 @with_all_phases
 @spec_test
 @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
     attestation = get_valid_attestation(spec, state, signed=True)
diff --git a/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_rewards_and_penalties.py b/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_rewards_and_penalties.py
index b4fc46b7d..dd3dae50a 100644
--- a/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_rewards_and_penalties.py
+++ b/test_libs/pyspec/eth2spec/test/phase_0/epoch_processing/test_process_rewards_and_penalties.py
@@ -1,7 +1,7 @@
 from copy import deepcopy
 
 from eth2spec.test.context import spec_state_test, with_all_phases, spec_test, \
-    misc_balances, with_custom_state, default_activation_threshold
+    misc_balances, with_custom_state, default_activation_threshold, single_phase
 from eth2spec.test.helpers.state import (
     next_epoch,
     next_slot,
@@ -96,6 +96,7 @@ def test_full_attestations(spec, state):
 @with_all_phases
 @spec_test
 @with_custom_state(balances_fn=misc_balances, threshold_fn=default_activation_threshold)
+@single_phase
 def test_full_attestations_misc_balances(spec, state):
     attestations = prepare_state_with_full_attestations(spec, state)