diff --git a/specs/phase0/beacon-chain.md b/specs/phase0/beacon-chain.md
index cdf38dc1e..1fd18336d 100644
--- a/specs/phase0/beacon-chain.md
+++ b/specs/phase0/beacon-chain.md
@@ -1219,7 +1219,7 @@ def verify_block_signature(state: BeaconState, signed_block: SignedBeaconBlock)
 
 ```python
 def process_slots(state: BeaconState, slot: Slot) -> None:
-    assert state.slot <= slot
+    assert state.slot < slot
     while state.slot < slot:
         process_slot(state)
         # Process epoch on the start slot of the next epoch
diff --git a/tests/core/pyspec/eth2spec/test/helpers/attestations.py b/tests/core/pyspec/eth2spec/test/helpers/attestations.py
index 8215f5c5b..76e90e89f 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/attestations.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/attestations.py
@@ -243,7 +243,8 @@ def fill_aggregate_attestation(spec, state, attestation, signed=False):
 
 
 def add_attestations_to_state(spec, state, attestations, slot):
-    spec.process_slots(state, slot)
+    if state.slot < slot:
+        spec.process_slots(state, slot)
     for attestation in attestations:
         spec.process_attestation(state, attestation)
 
diff --git a/tests/core/pyspec/eth2spec/test/helpers/block.py b/tests/core/pyspec/eth2spec/test/helpers/block.py
index 96cc30e35..b6167c569 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/block.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/block.py
@@ -15,7 +15,8 @@ def get_proposer_index_maybe(spec, state, slot, proposer_index=None):
                       " Signing block is slow due to transition for proposer index calculation.")
             # use stub state to get proposer index of future slot
             stub_state = state.copy()
-            spec.process_slots(stub_state, slot)
+            if stub_state.slot < slot:
+                spec.process_slots(stub_state, slot)
             proposer_index = spec.get_beacon_proposer_index(stub_state)
     return proposer_index
 
@@ -52,7 +53,10 @@ def sign_block(spec, state, block, proposer_index=None):
 
 
 def transition_unsigned_block(spec, state, block):
-    spec.process_slots(state, block.slot)
+    if state.slot < block.slot:
+        spec.process_slots(state, block.slot)
+    assert state.latest_block_header.slot < block.slot  # There may not already be a block in this slot or past it.
+    assert state.slot == block.slot  # The block must be for this slot
     spec.process_block(state, block)
 
 
@@ -74,9 +78,10 @@ def build_empty_block(spec, state, slot=None):
     if slot < state.slot:
         raise Exception("build_empty_block cannot build blocks for past slots")
     if slot > state.slot:
-        # transition forward in copied state to grab relevant data from state
-        state = state.copy()
-        spec.process_slots(state, slot)
+        if state.slot < slot:
+            # transition forward in copied state to grab relevant data from state
+            state = state.copy()
+            spec.process_slots(state, slot)
 
     empty_block = spec.BeaconBlock()
     empty_block.slot = slot
diff --git a/tests/core/pyspec/eth2spec/test/helpers/state.py b/tests/core/pyspec/eth2spec/test/helpers/state.py
index 46a7ce2b5..3860a11ce 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/state.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/state.py
@@ -17,7 +17,8 @@ def next_slots(spec, state, slots):
     """
     Transition given slots forward.
     """
-    spec.process_slots(state, state.slot + slots)
+    if slots > 0:
+        spec.process_slots(state, state.slot + slots)
 
 
 def transition_to(spec, state, slot):
@@ -35,7 +36,8 @@ def next_epoch(spec, state):
     Transition to the start slot of the next epoch
     """
     slot = state.slot + spec.SLOTS_PER_EPOCH - (state.slot % spec.SLOTS_PER_EPOCH)
-    spec.process_slots(state, slot)
+    if slot > state.slot:
+        spec.process_slots(state, slot)
 
 
 def get_state_root(spec, state, slot) -> bytes:
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/run_epoch_process_base.py b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/run_epoch_process_base.py
index af4587a2a..b8692227f 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/run_epoch_process_base.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/epoch_processing/run_epoch_process_base.py
@@ -18,7 +18,8 @@ def run_epoch_processing_to(spec, state, process_name: str):
     slot = state.slot + (spec.SLOTS_PER_EPOCH - state.slot % spec.SLOTS_PER_EPOCH)
 
     # transition state to slot before epoch state transition
-    spec.process_slots(state, slot - 1)
+    if state.slot < slot - 1:
+        spec.process_slots(state, slot - 1)
 
     # start transitioning, do one slot update before the epoch itself.
     spec.process_slot(state)
diff --git a/tests/core/pyspec/eth2spec/test/sanity/test_slots.py b/tests/core/pyspec/eth2spec/test/sanity/test_slots.py
index 6ef6be4d3..dd4f302ae 100644
--- a/tests/core/pyspec/eth2spec/test/sanity/test_slots.py
+++ b/tests/core/pyspec/eth2spec/test/sanity/test_slots.py
@@ -51,7 +51,8 @@ def test_double_empty_epoch(spec, state):
 @with_all_phases
 @spec_state_test
 def test_over_epoch_boundary(spec, state):
-    spec.process_slots(state, state.slot + (spec.SLOTS_PER_EPOCH // 2))
+    if spec.SLOTS_PER_EPOCH > 1:
+        spec.process_slots(state, state.slot + (spec.SLOTS_PER_EPOCH // 2))
     yield 'pre', state
     slots = spec.SLOTS_PER_EPOCH
     yield 'slots', slots