diff --git a/tests/core/pyspec/eth2spec/test/phase0/block_processing/test_process_voluntary_exit.py b/tests/core/pyspec/eth2spec/test/phase0/block_processing/test_process_voluntary_exit.py
index 1b6b40580..9e209f23e 100644
--- a/tests/core/pyspec/eth2spec/test/phase0/block_processing/test_process_voluntary_exit.py
+++ b/tests/core/pyspec/eth2spec/test/phase0/block_processing/test_process_voluntary_exit.py
@@ -1,6 +1,7 @@
+from eth2spec.test.helpers.constants import MINIMAL
 from eth2spec.test.context import (
     spec_state_test, expect_assertion_error,
-    always_bls, with_all_phases,
+    always_bls, with_all_phases, with_presets,
     spec_test, single_phase,
     with_custom_state, scaled_churn_balances,
 )
@@ -123,6 +124,8 @@ def test_success_exit_queue__min_churn(spec, state):
 
 
 @with_all_phases
+@with_presets([MINIMAL],
+              reason="mainnet config leads to larger validator set than limit of public/private keys pre-generated")
 @spec_test
 @with_custom_state(balances_fn=scaled_churn_balances, threshold_fn=lambda spec: spec.config.EJECTION_BALANCE)
 @single_phase
diff --git a/tests/core/pyspec/eth2spec/test/phase0/epoch_processing/test_process_registry_updates.py b/tests/core/pyspec/eth2spec/test/phase0/epoch_processing/test_process_registry_updates.py
index 6b1d7bce9..5bcf3a82b 100644
--- a/tests/core/pyspec/eth2spec/test/phase0/epoch_processing/test_process_registry_updates.py
+++ b/tests/core/pyspec/eth2spec/test/phase0/epoch_processing/test_process_registry_updates.py
@@ -1,9 +1,10 @@
 from eth2spec.test.helpers.deposits import mock_deposit
 from eth2spec.test.helpers.state import next_epoch, next_slots
+from eth2spec.test.helpers.constants import MINIMAL
 from eth2spec.test.context import (
     spec_test, spec_state_test,
     with_all_phases, single_phase,
-    with_custom_state,
+    with_custom_state, with_presets,
     scaled_churn_balances,
 )
 from eth2spec.test.helpers.epoch_processing import run_epoch_processing_with
@@ -160,6 +161,8 @@ def test_activation_queue_efficiency_min(spec, state):
 
 
 @with_all_phases
+@with_presets([MINIMAL],
+              reason="mainnet config leads to larger validator set than limit of public/private keys pre-generated")
 @spec_test
 @with_custom_state(balances_fn=scaled_churn_balances, threshold_fn=lambda spec: spec.config.EJECTION_BALANCE)
 @single_phase
@@ -221,6 +224,8 @@ def test_ejection_past_churn_limit_min(spec, state):
 
 
 @with_all_phases
+@with_presets([MINIMAL],
+              reason="mainnet config leads to larger validator set than limit of public/private keys pre-generated")
 @spec_test
 @with_custom_state(balances_fn=scaled_churn_balances, threshold_fn=lambda spec: spec.config.EJECTION_BALANCE)
 @single_phase
@@ -314,6 +319,8 @@ def test_activation_queue_activation_and_ejection__exceed_churn_limit(spec, stat
 
 
 @with_all_phases
+@with_presets([MINIMAL],
+              reason="mainnet config leads to larger validator set than limit of public/private keys pre-generated")
 @spec_test
 @with_custom_state(balances_fn=scaled_churn_balances, threshold_fn=lambda spec: spec.config.EJECTION_BALANCE)
 @single_phase
@@ -324,6 +331,8 @@ def test_activation_queue_activation_and_ejection__scaled_churn_limit(spec, stat
 
 
 @with_all_phases
+@with_presets([MINIMAL],
+              reason="mainnet config leads to larger validator set than limit of public/private keys pre-generated")
 @spec_test
 @with_custom_state(balances_fn=scaled_churn_balances, threshold_fn=lambda spec: spec.config.EJECTION_BALANCE)
 @single_phase