diff --git a/tests/core/pyspec/eth2spec/test/helpers/rewards.py b/tests/core/pyspec/eth2spec/test/helpers/rewards.py
index 42e7a7614..d62fee6ce 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/rewards.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/rewards.py
@@ -174,6 +174,9 @@ def set_some_new_deposits(spec, state, rng):
     num_validators = len(state.validators)
     # Set ~1/10 to just recently deposited
     for index in range(num_validators):
+        # If not already active, skip
+        if not spec.is_active_validator(state.validators[index], spec.get_current_epoch(state)):
+            continue
         if rng.randrange(num_validators) < num_validators // 10:
             mock_deposit(spec, state, index)
             # Set ~half of selected to eligible for activation
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/rewards/test_random.py b/tests/core/pyspec/eth2spec/test/phase_0/rewards/test_random.py
index bda0ca687..83c7f7905 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/rewards/test_random.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/rewards/test_random.py
@@ -1,6 +1,13 @@
 from random import Random
 
-from eth2spec.test.context import with_all_phases, spec_state_test
+from eth2spec.test.context import (
+    with_all_phases,
+    spec_test,
+    spec_state_test,
+    with_custom_state,
+    single_phase,
+    low_balances, misc_balances,
+)
 import eth2spec.test.helpers.rewards as rewards_helpers
 
 
@@ -20,3 +27,19 @@ def test_full_random_1(spec, state):
 @spec_state_test
 def test_full_random_2(spec, state):
     yield from rewards_helpers.run_test_full_random(spec, state, rng=Random(3030))
+
+
+@with_all_phases
+@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):
+    yield from rewards_helpers.run_test_full_random(spec, state)
+
+
+@with_all_phases
+@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):
+    yield from rewards_helpers.run_test_full_random(spec, state)