diff --git a/spinoffs/fun_mc/fun_mc/dynamic/backend_jax/util.py b/spinoffs/fun_mc/fun_mc/dynamic/backend_jax/util.py
index 0a88d94f6a..cd9ea3e493 100644
--- a/spinoffs/fun_mc/fun_mc/dynamic/backend_jax/util.py
+++ b/spinoffs/fun_mc/fun_mc/dynamic/backend_jax/util.py
@@ -169,8 +169,12 @@ def random_categorical(logits, num_samples, seed):
 def trace(state, fn, num_steps, unroll, max_steps, **_):
   """Implementation of `trace` operator, without the calling convention."""
   # We need the shapes and dtypes of the outputs of `fn`.
-  _, untraced_spec, traced_spec = jax.eval_shape(
+  _, untraced_spec, traced_spec, stop_spec = jax.eval_shape(
       fn, map_tree(lambda s: jax.ShapeDtypeStruct(s.shape, s.dtype), state))
+  if isinstance(stop_spec, tuple):
+    stop = ()
+  else:
+    stop = False
   untraced_init, traced_init = map_tree(
       lambda spec: jnp.zeros(spec.shape, spec.dtype),
       (untraced_spec, traced_spec),
@@ -194,7 +198,7 @@ def trace(state, fn, num_steps, unroll, max_steps, **_):
             'Cannot unroll when `num_steps` is not statically known and '
             '`max_steps` is not specified.'
         )
-  if max_steps is not None:
+  if max_steps is not None or not isinstance(stop_spec, tuple):
     use_scan = False
 
   if unroll:
@@ -203,8 +207,8 @@ def trace(state, fn, num_steps, unroll, max_steps, **_):
     traced_lists = map_tree(lambda _: [], traced_spec)
     untraced = untraced_init
     for step in range(num_outputs):
-      if step < num_steps:
-        state, untraced, traced_element = fn(state)
+      if step < num_steps and not stop:
+        state, untraced, traced_element, stop = fn(state)
       else:
         traced_element = traced_init
       map_tree_up_to(traced_spec, lambda l, e: l.append(e), traced_lists,
@@ -217,7 +221,7 @@ def trace(state, fn, num_steps, unroll, max_steps, **_):
 
     def wrapper(state_untraced, _):
       state, _ = state_untraced
-      state, untraced, traced = fn(state)
+      state, untraced, traced, _ = fn(state)
       return (state, untraced), traced
 
     (state, untraced), traced = lax.scan(
@@ -234,19 +238,31 @@ def wrapper(state_untraced, _):
 
     trace_arrays = map_tree(
         lambda spec: jnp.zeros((num_outputs,) + spec.shape, spec.dtype),
-        traced_spec)
+        traced_spec,
+    )
+    loop_vars = (
+        jnp.zeros_like(num_steps),
+        stop,
+        state,
+        untraced_init,
+        trace_arrays,
+    )
 
-    def wrapper(i, state_untraced_traced):
-      state, _, trace_arrays = state_untraced_traced
-      state, untraced, traced = fn(state)
+    def cond(loop_vars):
+      i, stop, *_ = loop_vars
+      return (i < num_steps) & (isinstance(stop, tuple) or ~stop)
+
+    def body(loop_vars):
+      i, _, state, _, trace_arrays = loop_vars
+      state, untraced, traced, stop = fn(state)
       trace_arrays = map_tree(lambda a, e: a.at[i].set(e), trace_arrays, traced)
-      return (state, untraced, trace_arrays)
 
-    state, untraced, traced = lax.fori_loop(
-        jnp.asarray(0, num_steps.dtype),
-        num_steps,
-        wrapper,
-        (state, untraced_init, trace_arrays),
+      return i + 1, stop, state, untraced, trace_arrays
+
+    _, _, state, untraced, traced = lax.while_loop(
+        cond,
+        body,
+        loop_vars,
     )
   return state, untraced, traced
 
diff --git a/spinoffs/fun_mc/fun_mc/dynamic/backend_tensorflow/util.py b/spinoffs/fun_mc/fun_mc/dynamic/backend_tensorflow/util.py
index cb3cd8ae6e..92d0a5c275 100644
--- a/spinoffs/fun_mc/fun_mc/dynamic/backend_tensorflow/util.py
+++ b/spinoffs/fun_mc/fun_mc/dynamic/backend_tensorflow/util.py
@@ -182,7 +182,7 @@ def trace(state, fn, num_steps, unroll, max_steps, parallel_iterations=10):
   num_outputs = num_steps if max_steps is None else max_steps
 
   if tf.config.experimental_functions_run_eagerly() or tf.executing_eagerly():
-    state, first_untraced, first_traced = fn(state)
+    state, first_untraced, first_traced, stop = fn(state)
     arrays = tf.nest.map_structure(
         lambda v: tf.TensorArray(  # pylint: disable=g-long-lambda
             v.dtype,
@@ -195,7 +195,7 @@ def trace(state, fn, num_steps, unroll, max_steps, parallel_iterations=10):
     # the `TensorArray`s etc., we can get it by pre-compiling the wrapper
     # function.
     input_spec = tf.nest.map_structure(tf.TensorSpec.from_tensor, state)
-    fn, (_, untraced_spec, traced_spec) = _eval_shape(fn, input_spec)
+    fn, (_, untraced_spec, traced_spec, stop_spec) = _eval_shape(fn, input_spec)
 
     arrays = tf.nest.map_structure(
         lambda spec: tf.TensorArray(  # pylint: disable=g-long-lambda
@@ -206,18 +206,23 @@ def trace(state, fn, num_steps, unroll, max_steps, parallel_iterations=10):
     first_untraced = tf.nest.map_structure(
         lambda spec: tf.zeros(spec.shape, spec.dtype), untraced_spec)
     start_idx = 0
+    if isinstance(stop_spec, tuple):
+      stop = ()
+    else:
+      stop = False
 
-  def body(i, state, _, arrays):
-    state, untraced, traced = fn(state)
+  def body(i, stop, state, untraced, arrays):
+    del stop, untraced
+    state, untraced, traced, stop = fn(state)
     arrays = tf.nest.map_structure(lambda a, e: a.write(i, e), arrays, traced)
-    return i + 1, state, untraced, arrays
+    return i + 1, stop, state, untraced, arrays
 
-  def cond(i, *_):
-    return i < num_steps
+  def cond(i, stop, *_):
+    return (i < num_steps) & (isinstance(stop, tuple) or ~stop)
 
   static_num_steps = tf.get_static_value(num_steps)
   static_num_outputs = tf.get_static_value(num_outputs)
-  loop_vars = (start_idx, state, first_untraced, arrays)
+  loop_vars = (start_idx, stop, state, first_untraced, arrays)
 
   if unroll:
     if static_num_steps is None:
@@ -233,8 +238,10 @@ def cond(i, *_):
     # TODO(siege): Investigate if using lists instead of TensorArray's is faster
     # (like is done in the JAX backend).
     for _ in range(start_idx, static_num_iters):
+      if loop_vars[1]:
+        break
       loop_vars = body(*loop_vars)
-    _, state, untraced, arrays = loop_vars
+    _, _, state, untraced, arrays = loop_vars
   else:
     if static_num_steps is None:
       if max_steps is None:
@@ -246,7 +253,7 @@ def cond(i, *_):
         maximum_iterations = static_num_steps - start_idx
       else:
         maximum_iterations = min(static_num_steps, max_steps) - start_idx
-    _, state, untraced, arrays = tf.while_loop(
+    _, _, state, untraced, arrays = tf.while_loop(
         cond=cond,
         body=body,
         loop_vars=loop_vars,
diff --git a/spinoffs/fun_mc/fun_mc/fun_mc_lib.py b/spinoffs/fun_mc/fun_mc/fun_mc_lib.py
index 03069a14f1..afc87faa38 100644
--- a/spinoffs/fun_mc/fun_mc/fun_mc_lib.py
+++ b/spinoffs/fun_mc/fun_mc/fun_mc_lib.py
@@ -221,6 +221,7 @@ def trace(
     trace_mask: bool | BooleanNest = True,
     unroll: bool = False,
     max_steps: int | None = None,
+    stop_fn: Callable[[State, ArrayNest], BooleanArray] | None = None,
     parallel_iterations: int = 10,
 ) -> tuple[State, ArrayNest]:
   """`TransitionOperator` that runs `fn` repeatedly and traces its outputs.
@@ -245,8 +246,11 @@ def trace(
       performance at the cost of increasing the XLA optimization time. Only
       works if `num_steps` is statically known.
     max_steps: If `num_steps` is not statically known and you still want to
-      trace values, you can use `max_steps` to allocate output trace to be of
-      this length. Only elements up to `num_steps` will be valid, however.
+      values, you can use `max_steps` to allocate output trace to be of this
+      length. Only elements up to `num_steps` will be valid, however.
+    stop_fn: Optional callable that takes in the outputs of `fn` and returns a
+      boolean. If `True`, then the iteration is stopped. Only the elements
+      stored into traces before `stop_fn` returned `True` are valid.
     parallel_iterations: Number of iterations of the while loop to run in
       parallel (TensorFlow-only).
 
@@ -286,11 +290,17 @@ def wrapper(state):
     state, extra = util.map_tree(
         util.convert_to_tensor, call_transition_operator(fn, state)
     )
+    if stop_fn is None:
+      # For TF compatibility, we can't use None. () is conveniently "falsy",
+      # which we rely on in the backend implementations.
+      stop = ()
+    else:
+      stop = stop_fn(state, extra)
     trace_element = util.map_tree(
         util.convert_to_tensor, trace_fn(state, extra)
     )
     untraced, traced = _split_trace(trace_element, trace_mask)
-    return state, untraced, traced
+    return state, untraced, traced, stop
 
   state = util.map_tree(util.convert_to_tensor, state)
 
diff --git a/spinoffs/fun_mc/fun_mc/fun_mc_test.py b/spinoffs/fun_mc/fun_mc/fun_mc_test.py
index 21382bf439..cb743a9a20 100644
--- a/spinoffs/fun_mc/fun_mc/fun_mc_test.py
+++ b/spinoffs/fun_mc/fun_mc/fun_mc_test.py
@@ -243,6 +243,42 @@ def testTraceMaxSteps(self, unroll):
     self.assertEqual(6, traced.shape[0])
     self.assertAllEqual(400, untraced)
 
+  @parameterized.named_parameters(
+      ('Unrolled', True),
+      ('NotUnrolled', False),
+  )
+  def testTraceStopFnSingle(self, unroll):
+    x, (traced, untraced) = fun_mc.trace(
+        0,
+        lambda x: (x + 1, (10 * x, 100 * x)),
+        5,
+        unroll=unroll,
+        trace_mask=(True, False),
+        stop_fn=lambda x, _: x == 1,
+    )
+    self.assertAllEqual(1, x)
+    self.assertAllEqual(0, traced[0])
+    self.assertEqual(5, traced.shape[0])
+    self.assertAllEqual(0, untraced)
+
+  @parameterized.named_parameters(
+      ('Unrolled', True),
+      ('NotUnrolled', False),
+  )
+  def testTraceStopFnMulti(self, unroll):
+    x, (traced, untraced) = fun_mc.trace(
+        0,
+        lambda x: (x + 1, (10 * x, 100 * x)),
+        5,
+        unroll=unroll,
+        trace_mask=(True, False),
+        stop_fn=lambda x, _: x == 3,
+    )
+    self.assertAllEqual(3, x)
+    self.assertAllEqual(20, traced[2])
+    self.assertEqual(5, traced.shape[0])
+    self.assertAllEqual(200, untraced)
+
   @parameterized.named_parameters(
       ('Unrolled', True),
       ('NotUnrolled', False),