diff --git a/tests/core/pyspec/eth2spec/test/context.py b/tests/core/pyspec/eth2spec/test/context.py
index c2bbff341..7f58c6610 100644
--- a/tests/core/pyspec/eth2spec/test/context.py
+++ b/tests/core/pyspec/eth2spec/test/context.py
@@ -329,12 +329,15 @@ def disable_process_reveal_deadlines(fn):
     return with_meta_tags({'reveal_deadlines_setting': 1})(entry)
 
 
-def with_configs(configs):
+def with_configs(configs, reason=None):
     def decorator(fn):
         def wrapper(*args, spec: Spec, **kw):
             available_configs = set(configs)
             if spec.CONFIG_NAME not in available_configs:
-                dump_skipping_message(f"doesn't support this config: {spec.CONFIG_NAME}")
+                message = f"doesn't support this config: {spec.CONFIG_NAME}."
+                if reason is not None:
+                    message = f"{message} Reason: {reason}"
+                dump_skipping_message(message)
                 return None
 
             return fn(*args, spec=spec, **kw)
diff --git a/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_chunk_challenge.py b/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_chunk_challenge.py
index ecc704184..e916010b2 100644
--- a/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_chunk_challenge.py
+++ b/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_chunk_challenge.py
@@ -9,10 +9,12 @@ from eth2spec.test.helpers.attestations import (
 from eth2spec.test.helpers.state import transition_to, transition_to_valid_shard_slot
 from eth2spec.test.context import (
     PHASE0,
+    MINIMAL,
     expect_assertion_error,
     disable_process_reveal_deadlines,
     spec_state_test,
     with_all_phases_except,
+    with_configs,
 )
 from eth2spec.test.phase0.block_processing.test_process_attestation import run_attestation_processing
 
@@ -68,6 +70,7 @@ def run_custody_chunk_response_processing(spec, state, custody_response, valid=T
 
 @with_all_phases_except([PHASE0])
 @spec_state_test
+@with_configs([MINIMAL], reason="too slow")
 @disable_process_reveal_deadlines
 def test_challenge_appended(spec, state):
     transition_to_valid_shard_slot(spec, state)
@@ -92,6 +95,7 @@ def test_challenge_appended(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_challenge_empty_element_replaced(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + 1)  # Make len(offset_slots) == 1
@@ -117,6 +121,7 @@ def test_challenge_empty_element_replaced(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_duplicate_challenge(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + 1)  # Make len(offset_slots) == 1
@@ -142,6 +147,7 @@ def test_duplicate_challenge(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_second_challenge(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + 1)  # Make len(offset_slots) == 1
@@ -169,6 +175,7 @@ def test_second_challenge(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_multiple_epochs_custody(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH * 3)
@@ -193,6 +200,7 @@ def test_multiple_epochs_custody(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_many_epochs_custody(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH * 20)
@@ -217,6 +225,7 @@ def test_many_epochs_custody(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_off_chain_attestation(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH)
@@ -237,6 +246,7 @@ def test_off_chain_attestation(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_custody_response(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH)
@@ -268,6 +278,7 @@ def test_custody_response(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_custody_response_chunk_index_2(spec, state):
     transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH)
 
@@ -298,6 +309,7 @@ def test_custody_response_chunk_index_2(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_custody_response_multiple_epochs(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH * 3)
@@ -329,6 +341,7 @@ def test_custody_response_multiple_epochs(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_custody_response_many_epochs(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH * 20)
diff --git a/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_custody_slashing.py b/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_custody_slashing.py
index 6836685b8..fc7efa5bc 100644
--- a/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_custody_slashing.py
+++ b/tests/core/pyspec/eth2spec/test/phase1/block_processing/test_process_custody_slashing.py
@@ -10,10 +10,12 @@ from eth2spec.utils.ssz.ssz_typing import ByteList
 from eth2spec.test.helpers.state import get_balance, transition_to
 from eth2spec.test.context import (
     PHASE0,
+    MINIMAL,
     with_all_phases_except,
     spec_state_test,
     expect_assertion_error,
     disable_process_reveal_deadlines,
+    with_configs,
 )
 from eth2spec.test.phase0.block_processing.test_process_attestation import run_attestation_processing
 
@@ -113,6 +115,7 @@ def run_standard_custody_slashing_test(spec,
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_custody_slashing(spec, state):
     yield from run_standard_custody_slashing_test(spec, state)
 
@@ -120,6 +123,7 @@ def test_custody_slashing(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_incorrect_custody_slashing(spec, state):
     yield from run_standard_custody_slashing_test(spec, state, correct=False)
 
@@ -127,6 +131,7 @@ def test_incorrect_custody_slashing(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_multiple_epochs_custody(spec, state):
     yield from run_standard_custody_slashing_test(spec, state, shard_lateness=spec.SLOTS_PER_EPOCH * 3)
 
@@ -134,6 +139,7 @@ def test_multiple_epochs_custody(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_many_epochs_custody(spec, state):
     yield from run_standard_custody_slashing_test(spec, state, shard_lateness=spec.SLOTS_PER_EPOCH * 5)
 
@@ -141,6 +147,7 @@ def test_many_epochs_custody(spec, state):
 @with_all_phases_except([PHASE0])
 @spec_state_test
 @disable_process_reveal_deadlines
+@with_configs([MINIMAL], reason="too slow")
 def test_invalid_custody_slashing(spec, state):
     yield from run_standard_custody_slashing_test(
         spec,
diff --git a/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_challenge_deadlines.py b/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_challenge_deadlines.py
index 828ace91c..e270ff615 100644
--- a/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_challenge_deadlines.py
+++ b/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_challenge_deadlines.py
@@ -8,8 +8,10 @@ from eth2spec.test.helpers.attestations import (
 from eth2spec.test.helpers.state import transition_to, transition_to_valid_shard_slot
 from eth2spec.test.context import (
     PHASE0,
-    with_all_phases_except,
+    MINIMAL,
     spec_state_test,
+    with_all_phases_except,
+    with_configs,
 )
 from eth2spec.test.phase0.block_processing.test_process_attestation import run_attestation_processing
 from eth2spec.test.phase0.epoch_processing.run_epoch_process_base import run_epoch_processing_with
@@ -25,6 +27,7 @@ def run_process_challenge_deadlines(spec, state):
 
 @with_all_phases_except([PHASE0])
 @spec_state_test
+@with_configs([MINIMAL], reason="too slow")
 def test_validator_slashed_after_chunk_challenge(spec, state):
     transition_to_valid_shard_slot(spec, state)
     transition_to(spec, state, state.slot + 1)  # Make len(offset_slots) == 1
diff --git a/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_reveal_deadlines.py b/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_reveal_deadlines.py
index da1a60446..5777e184a 100644
--- a/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_reveal_deadlines.py
+++ b/tests/core/pyspec/eth2spec/test/phase1/epoch_processing/test_process_reveal_deadlines.py
@@ -4,7 +4,9 @@ from eth2spec.test.helpers.custody import (
 from eth2spec.test.helpers.state import transition_to
 from eth2spec.test.context import (
     PHASE0,
+    MINIMAL,
     with_all_phases_except,
+    with_configs,
     spec_state_test,
 )
 from eth2spec.test.phase0.epoch_processing.run_epoch_process_base import run_epoch_processing_with
@@ -17,6 +19,7 @@ def run_process_challenge_deadlines(spec, state):
 
 @with_all_phases_except([PHASE0])
 @spec_state_test
+@with_configs([MINIMAL], reason="too slow")
 def test_validator_slashed_after_reveal_deadline(spec, state):
     assert state.validators[0].slashed == 0
     transition_to(spec, state, spec.get_randao_epoch_for_custody_period(0, 0) * spec.SLOTS_PER_EPOCH)
@@ -36,6 +39,7 @@ def test_validator_slashed_after_reveal_deadline(spec, state):
 
 @with_all_phases_except([PHASE0])
 @spec_state_test
+@with_configs([MINIMAL], reason="too slow")
 def test_validator_not_slashed_after_reveal(spec, state):
     transition_to(spec, state, spec.EPOCHS_PER_CUSTODY_PERIOD * spec.SLOTS_PER_EPOCH)
     custody_key_reveal = get_valid_custody_key_reveal(spec, state)