diff --git a/cirq-core/cirq/circuits/circuit.py b/cirq-core/cirq/circuits/circuit.py
index f1dd45369eb..3415337a49f 100644
--- a/cirq-core/cirq/circuits/circuit.py
+++ b/cirq-core/cirq/circuits/circuit.py
@@ -1618,6 +1618,7 @@ class Circuit(AbstractCircuit):
     AbstractCircuit):
 
     *   next_moment_operating_on
+    *   earliest_available_moment
     *   prev_moment_operating_on
     *   next_moments_operating_on
     *   operation_at
@@ -1950,7 +1951,27 @@ def transform_qubits(
         with _compat.block_overlapping_deprecation(re.escape(_DEVICE_DEP_MESSAGE)):
             return Circuit(op_list, device=self._device if new_device is None else new_device)
 
-    def _prev_moment_available(self, op: 'cirq.Operation', end_moment_index: int) -> Optional[int]:
+    def earliest_available_moment(
+        self, op: 'cirq.Operation', *, end_moment_index: Optional[int] = None
+    ) -> int:
+        """Finds the index of the earliest (i.e. left most) moment which can accommodate `op`.
+
+        Note that, unlike `circuit.prev_moment_operating_on`, this method also takes care of
+        implicit dependencies between measurements and classically controlled operations (CCO)
+        that depend on the results of those measurements. Therefore, using this method, a CCO
+        `op` would not be allowed to move left past a measurement it depends upon.
+
+        Args:
+            op: Operation for which the earliest moment that can accommodate it needs to be found.
+            end_moment_index: The moment index just after the starting point of the reverse search.
+                Defaults to the length of the list of moments.
+
+        Returns:
+            Index of the earliest matching moment. Returns `end_moment_index` if no moment on left
+            is available.
+        """
+        if end_moment_index is None:
+            end_moment_index = len(self.moments)
         last_available = end_moment_index
         k = end_moment_index
         op_control_keys = protocols.control_keys(op)
@@ -1968,6 +1989,8 @@ def _prev_moment_available(self, op: 'cirq.Operation', end_moment_index: int) ->
             ):
                 return last_available
             if self._can_add_op_at(k, op):
+                # Note: Remove the if condition after `self._device` is gone and move the method to
+                # `cirq.AbstractDevice`.
                 last_available = k
         return last_available
 
@@ -2005,8 +2028,7 @@ def _pick_or_create_inserted_op_moment_index(
 
         if strategy is InsertStrategy.EARLIEST:
             if self._can_add_op_at(splitter_index, op):
-                p = self._prev_moment_available(op, splitter_index)
-                return p or 0
+                return self.earliest_available_moment(op, end_moment_index=splitter_index)
 
             return self._pick_or_create_inserted_op_moment_index(
                 splitter_index, op, InsertStrategy.INLINE
diff --git a/cirq-core/cirq/circuits/circuit_test.py b/cirq-core/cirq/circuits/circuit_test.py
index 76e5262dd3a..aedfa273d51 100644
--- a/cirq-core/cirq/circuits/circuit_test.py
+++ b/cirq-core/cirq/circuits/circuit_test.py
@@ -1402,6 +1402,28 @@ def test_prev_moment_operating_on_distance(circuit_cls):
         c.prev_moment_operating_on([a], 6, max_distance=-1)
 
 
+def test_earliest_available_moment():
+    q = cirq.LineQubit.range(3)
+    c = cirq.Circuit(
+        cirq.Moment(cirq.measure(q[0], key="m")),
+        cirq.Moment(cirq.X(q[1]).with_classical_controls("m")),
+    )
+    assert c.earliest_available_moment(cirq.Y(q[0])) == 1
+    assert c.earliest_available_moment(cirq.Y(q[1])) == 2
+    assert c.earliest_available_moment(cirq.Y(q[2])) == 0
+    assert c.earliest_available_moment(cirq.Y(q[2]).with_classical_controls("m")) == 1
+    assert (
+        c.earliest_available_moment(cirq.Y(q[2]).with_classical_controls("m"), end_moment_index=1)
+        == 1
+    )
+
+    # Returns `end_moment_index` by default without verifying if an operation already exists there.
+    assert (
+        c.earliest_available_moment(cirq.Y(q[1]).with_classical_controls("m"), end_moment_index=1)
+        == 1
+    )
+
+
 @pytest.mark.parametrize('circuit_cls', [cirq.Circuit, cirq.FrozenCircuit])
 def test_operation_at(circuit_cls):
     a = cirq.NamedQubit('a')
diff --git a/cirq-core/cirq/transformers/stratify.py b/cirq-core/cirq/transformers/stratify.py
index ac0866f9a84..dad3e3bdaee 100644
--- a/cirq-core/cirq/transformers/stratify.py
+++ b/cirq-core/cirq/transformers/stratify.py
@@ -152,8 +152,7 @@ def map_func(m: 'cirq.Moment', _) -> Sequence['cirq.Moment']:
         batch_removals: List[Tuple[int, 'cirq.Operation']] = []
         batch_inserts: List[Tuple[int, 'cirq.Operation']] = []
         for op in moment:
-            prv_idx = stratified_circuit._prev_moment_available(op, curr_idx)
-            prv_idx = 0 if prv_idx is None else prv_idx
+            prv_idx = stratified_circuit.earliest_available_moment(op, end_moment_index=curr_idx)
             prv_category = prv_idx % num_categories
             should_move_to_next_batch = curr_category < prv_category
             prv_idx += curr_category - prv_category + num_categories * should_move_to_next_batch