diff --git a/tests/core/pyspec/eth2spec/test/altair/transition/test_activations_and_exits.py b/tests/core/pyspec/eth2spec/test/altair/transition/test_activations_and_exits.py
index 2ccecec1a..25a76a686 100644
--- a/tests/core/pyspec/eth2spec/test/altair/transition/test_activations_and_exits.py
+++ b/tests/core/pyspec/eth2spec/test/altair/transition/test_activations_and_exits.py
@@ -39,7 +39,7 @@ def test_transition_with_one_fourth_exiting_validators_exit_post_fork(state,
         rng=random.Random(5566),
         fraction=0.25,
         exit_epoch=10,
-        forward=False,
+        from_epoch=spec.get_current_epoch(state),
     )
 
     transition_until_fork(spec, state, fork_epoch)
@@ -97,7 +97,7 @@ def test_transition_with_one_fourth_exiting_validators_exit_at_fork(state,
         rng=random.Random(5566),
         fraction=0.25,
         exit_epoch=fork_epoch,
-        forward=False,
+        from_epoch=spec.get_current_epoch(state),
     )
 
     transition_until_fork(spec, state, fork_epoch)
diff --git a/tests/core/pyspec/eth2spec/test/helpers/random.py b/tests/core/pyspec/eth2spec/test/helpers/random.py
index 4f6139989..1332d1e90 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/random.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/random.py
@@ -25,17 +25,18 @@ def set_some_new_deposits(spec, state, rng):
     return deposited_indices
 
 
-def exit_random_validators(spec, state, rng, fraction=0.5, exit_epoch=None, withdrawable_epoch=None, forward=True):
+def exit_random_validators(spec, state, rng, fraction=0.5, exit_epoch=None, withdrawable_epoch=None, from_epoch=None):
     """
     Set some validators' exit_epoch and withdrawable_epoch.
 
     If exit_epoch is configured, use the given exit_epoch. Otherwise, randomly set exit_epoch and withdrawable_epoch.
     """
-    if forward:
-        if spec.get_current_epoch(state) < 5:
-            # Move epochs forward to allow for some validators already exited/withdrawable
-            for _ in range(5):
-                next_epoch(spec, state)
+    if from_epoch is None:
+        from_epoch = spec.MAX_SEED_LOOKAHEAD + 1
+    epoch_diff = from_epoch - spec.get_current_epoch(state)
+    for _ in range(epoch_diff):
+        # NOTE: if `epoch_diff` is negative, then this loop body does not execute.
+        next_epoch(spec, state)
 
     current_epoch = spec.get_current_epoch(state)
     exited_indices = []