diff --git a/tests/core/pyspec/eth2spec/test/phase0/sanity/test_blocks_random.py b/tests/core/pyspec/eth2spec/test/phase0/sanity/test_blocks_random.py
index 52868c744..e0043332d 100644
--- a/tests/core/pyspec/eth2spec/test/phase0/sanity/test_blocks_random.py
+++ b/tests/core/pyspec/eth2spec/test/phase0/sanity/test_blocks_random.py
@@ -61,7 +61,11 @@ def _randomize_state(spec, state):
 ## epochs
 
 def _epochs_until_leak(spec):
-    return spec.MIN_EPOCHS_TO_INACTIVITY_PENALTY
+    """
+    State is "leaking" if the current epoch is at least
+    this value after the last finalized epoch.
+    """
+    return spec.MIN_EPOCHS_TO_INACTIVITY_PENALTY + 1
 
 
 def _epochs_for_shard_committee_period(spec):