diff --git a/tests/core/pyspec/eth2spec/test/altair/rewards/test_inactivity_scores.py b/tests/core/pyspec/eth2spec/test/altair/rewards/test_inactivity_scores.py
new file mode 100644
index 000000000..a523b5157
--- /dev/null
+++ b/tests/core/pyspec/eth2spec/test/altair/rewards/test_inactivity_scores.py
@@ -0,0 +1,121 @@
+from random import Random
+
+from eth2spec.test.context import (
+    with_altair_and_later,
+    spec_test,
+    spec_state_test,
+    with_custom_state,
+    single_phase,
+    low_balances, misc_balances,
+)
+from eth2spec.test.helpers.rewards import leaking
+import eth2spec.test.helpers.rewards as rewards_helpers
+
+
+def randomize_inactivity_scores(spec, state, minimum=0, maximum=50000, rng=Random(4242)):
+    state.inactivity_scores = [rng.randint(minimum, maximum) for _ in range(len(state.validators))]
+
+
+@with_altair_and_later
+@spec_state_test
+def test_random_inactivity_scores_0(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(9999))
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(9999))
+
+
+@with_altair_and_later
+@spec_state_test
+def test_random_inactivity_scores_1(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(10000))
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(10000))
+
+
+@with_altair_and_later
+@spec_state_test
+def test_half_zero_half_random_inactivity_scores(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(10101))
+    half_val_point = len(state.validators) // 2
+    state.inactivity_scores = [0] * half_val_point + state.inactivity_scores[half_val_point:]
+
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(10101))
+
+
+@with_altair_and_later
+@spec_state_test
+def test_random_high_inactivity_scores(spec, state):
+    randomize_inactivity_scores(spec, state, minimum=500000, maximum=5000000, rng=Random(9998))
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(9998))
+
+
+@with_altair_and_later
+@with_custom_state(balances_fn=low_balances, threshold_fn=lambda spec: spec.EJECTION_BALANCE)
+@spec_test
+@single_phase
+def test_random_inactivity_scores_low_balances_0(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(11111))
+    yield from rewards_helpers.run_test_full_random(spec, state)
+
+
+@with_altair_and_later
+@with_custom_state(balances_fn=low_balances, threshold_fn=lambda spec: 0)
+@spec_test
+@single_phase
+def test_random_inactivity_scores_low_balances_1(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(22222))
+    yield from rewards_helpers.run_test_full_random(spec, state)
+
+
+@with_altair_and_later
+@with_custom_state(balances_fn=misc_balances, threshold_fn=lambda spec: spec.EJECTION_BALANCE)
+@spec_test
+@single_phase
+def test_full_random_misc_balances(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(33333))
+    yield from rewards_helpers.run_test_full_random(spec, state)
+
+
+#
+# Leaking variants
+#
+
+@with_altair_and_later
+@spec_state_test
+@leaking()
+def test_random_inactivity_scores_leaking_0(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(9999))
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(9999))
+
+
+@with_altair_and_later
+@spec_state_test
+@leaking()
+def test_random_inactivity_scores_leaking_1(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(10000))
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(10000))
+
+
+@with_altair_and_later
+@spec_state_test
+@leaking()
+def test_half_zero_half_random_inactivity_scores_leaking(spec, state):
+    randomize_inactivity_scores(spec, state, rng=Random(10101))
+    half_val_point = len(state.validators) // 2
+    state.inactivity_scores = [0] * half_val_point + state.inactivity_scores[half_val_point:]
+
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(10101))
+
+
+@with_altair_and_later
+@spec_state_test
+@leaking()
+def test_random_high_inactivity_scores_leaking(spec, state):
+    randomize_inactivity_scores(spec, state, minimum=500000, maximum=5000000, rng=Random(9998))
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(9998))
+
+
+@with_altair_and_later
+@spec_state_test
+@leaking(epochs=5)
+def test_random_high_inactivity_scores_leaking_5_epochs(spec, state):
+    randomize_inactivity_scores(spec, state, minimum=500000, maximum=5000000, rng=Random(9998))
+    yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(9998))
diff --git a/tests/core/pyspec/eth2spec/test/phase0/rewards/test_random.py b/tests/core/pyspec/eth2spec/test/phase0/rewards/test_random.py
index ae44c6640..51bd27c14 100644
--- a/tests/core/pyspec/eth2spec/test/phase0/rewards/test_random.py
+++ b/tests/core/pyspec/eth2spec/test/phase0/rewards/test_random.py
@@ -39,7 +39,15 @@ def test_full_random_3(spec, state):
 @with_custom_state(balances_fn=low_balances, threshold_fn=lambda spec: spec.EJECTION_BALANCE)
 @spec_test
 @single_phase
-def test_full_random_low_balances(spec, state):
+def test_full_random_low_balances_0(spec, state):
+    yield from rewards_helpers.run_test_full_random(spec, state)
+
+
+@with_all_phases
+@with_custom_state(balances_fn=low_balances, threshold_fn=lambda spec: 0)
+@spec_test
+@single_phase
+def test_full_random_low_balances_1(spec, state):
     yield from rewards_helpers.run_test_full_random(spec, state)