diff --git a/jax/_src/lax/lax.py b/jax/_src/lax/lax.py
index b3e29eb95695..2f98b6daae6f 100644
--- a/jax/_src/lax/lax.py
+++ b/jax/_src/lax/lax.py
@@ -4181,10 +4181,19 @@ def _top_k_translation_rule(ctx, avals_in, avals_out, x, *, k):
 top_k_p.def_impl(partial(dispatch.apply_primitive, top_k_p))
 top_k_p.def_abstract_eval(_top_k_abstract_eval)
 def _top_k_lower(ctx, operand, k):
-  if not core.is_constant_dim(k):
+  if core.is_constant_dim(k):
+    return chlo.TopKOp(operand, mlir.i64_attr(k)).results
+  if xla_client.mlir_api_version < 54:
     # TODO: https://github.com/openxla/stablehlo/issues/1396
     raise ValueError("native serialization with shape polymorphism not implemented for top_k")
-  return chlo.TopKOp(operand, mlir.i64_attr(k)).results
+  k_value, = mlir.eval_dynamic_shape_as_vals(ctx, (k,))
+  out_values_aval, out_indices_aval, = ctx.avals_out
+  return mlir.custom_call(
+      "stablehlo.dynamic_top_k",
+      [mlir.aval_to_ir_type(out_values_aval),
+       mlir.aval_to_ir_type(out_indices_aval)],
+      [operand, k_value]).results
+
 mlir.register_lowering(top_k_p, _top_k_lower)
 ad.primitive_jvps[top_k_p] = _top_k_jvp
 batching.primitive_batchers[top_k_p] = _top_k_batch_rule
diff --git a/jax/experimental/jax2tf/jax_export.py b/jax/experimental/jax2tf/jax_export.py
index be2fb18dd348..39e621418678 100644
--- a/jax/experimental/jax2tf/jax_export.py
+++ b/jax/experimental/jax2tf/jax_export.py
@@ -697,12 +697,13 @@ def _check_lowering(lowering) -> None:
     # ApproxTopK on TPU
     "ApproxTopK",
     "tf.call_tf_function",  # From jax2tf.call_tf(func, call_tf_graph=True)
-    "tpu_custom_call",  # Pallas kernels
+    "tpu_custom_call",  # Pallas/TPU kernels
     # TODO(burmako): maintain backwards compatibility for these, until they
     # are upstreamed to StableHLO.
     # See https://github.com/openxla/stablehlo/issues/8.
     "stablehlo.dynamic_reduce_window",
     "stablehlo.dynamic_rng_bit_generator",
+    "stablehlo.dynamic_top_k",
     "shape_assertion",  # Used by shape_poly to evaluate assertions
 }
 
diff --git a/jax/experimental/jax2tf/tests/back_compat_test.py b/jax/experimental/jax2tf/tests/back_compat_test.py
index 1a56b5925227..69274c839301 100644
--- a/jax/experimental/jax2tf/tests/back_compat_test.py
+++ b/jax/experimental/jax2tf/tests/back_compat_test.py
@@ -51,6 +51,7 @@
 from jax.experimental.jax2tf.tests.back_compat_testdata import tpu_Sharding
 from jax.experimental.jax2tf.tests.back_compat_testdata import tpu_stablehlo_dynamic_reduce_window
 from jax.experimental.jax2tf.tests.back_compat_testdata import stablehlo_dynamic_rng_bit_generator
+from jax.experimental.jax2tf.tests.back_compat_testdata import stablehlo_dynamic_top_k
 
 from jax.experimental import pjit
 from jax.experimental.shard_map import shard_map
@@ -114,7 +115,9 @@ def test_custom_call_coverage(self):
         tpu_ApproxTopK.data_2023_05_16,
         tpu_stablehlo_dynamic_reduce_window.data_unary_2023_06_17,
         tpu_stablehlo_dynamic_reduce_window.data_variadic_2023_06_17,
-        stablehlo_dynamic_rng_bit_generator.data_2023_06_17,]
+        stablehlo_dynamic_rng_bit_generator.data_2023_06_17,
+        stablehlo_dynamic_top_k.data_2023_07_16,
+    ]
     # Some of the above are nested structures.
     covering_testdatas = itertools.chain(
         *[self.load_testdata_nested(d) for d in covering_testdatas])
@@ -129,7 +132,10 @@ def test_custom_call_coverage(self):
       "shape_assertion",
     })
     not_covered = targets_to_cover.difference(covered_targets)
-    self.assertEmpty(not_covered)
+    self.assertEmpty(not_covered,
+                     msg=("The following custom call targets are declared "
+                          "stable but are not covered by any tests: "
+                          f"{not_covered}"))
 
   def test_ducc_fft(self):
     def func(x):
@@ -672,6 +678,29 @@ def func(key, a):  # a is only used for its shape
     finally:
       jax.config.update("jax_default_prng_impl", prev_default_prng_impl)
 
+  def test_stablehlo_dynamic_top_k(self):
+    # stablehlo.dynamic_top_k is used temporarily for a top_k with dynamism
+    a = np.arange(12, dtype=np.float32).reshape((4, 3))
+
+    def func(a):
+      return lax.top_k(a, k=a.shape[-1] - 1)
+
+    data = self.load_testdata(stablehlo_dynamic_top_k.data_2023_07_16)
+    def check_top_k_results(res_run, res_expected, *, rtol, atol):
+      # The order of the results may be different, but should be the same ones
+      values_expected, _ = res_expected
+      values_run, indices_run = res_run
+      # Check that indices are correct
+      self.assertAllClose(values_run,
+                          a[np.arange(a.shape[0]).reshape(a.shape[0], 1),
+                            indices_run], atol=atol, rtol=rtol)
+      self.assertAllClose(np.sort(values_run), np.sort(values_expected),
+                          atol=atol, rtol=rtol)
+
+    self.run_one_test(func, data,
+                      polymorphic_shapes=("_, b",),
+                      check_results=check_top_k_results)
+
 
 if __name__ == "__main__":
   absltest.main(testLoader=jtu.JaxTestLoader())
diff --git a/jax/experimental/jax2tf/tests/back_compat_test_util.py b/jax/experimental/jax2tf/tests/back_compat_test_util.py
index 6f6fa97a9f4b..797c9fd6de35 100644
--- a/jax/experimental/jax2tf/tests/back_compat_test_util.py
+++ b/jax/experimental/jax2tf/tests/back_compat_test_util.py
@@ -40,19 +40,13 @@ def test_foo_call(self):
     def func(...): ...
     inputs = (...,)  # Tuple of nd.array, keep it small, perhaps generate the
                      # inputs in `func`.
-    data = dataclasses.replace(self.load_testdata(bctu.dummy_data_dict),
-                               inputs=inputs,
-                               platform=self.default_jax_backend())
-    self.run_one_test(func, data,
-                      # Temporarily allow calls to "foo"
-                      allow_additional_custom_call_targets=("foo",))
+    data = self.starter_data(inputs)  # This is temporary, just for starting.
+    self.run_one_test(func, data)
 
 The test will fail, but will save to a file the test data you will need. The
 file name will be printed in the logs. Create a new
 file ./back_compat_testdata/foo_call.py and paste the test data that
-you will see printed in the logs. You may want to
-edit the serialization string to remove any pathnames that may be included at
-the end, or gxxxxx3 at the beginning.
+you will see printed in the logs.
 
 Name the literal `data_YYYYY_MM_DD` to include the date of serializaton
 (for readability only). Then add to this file:
@@ -137,6 +131,13 @@ def default_jax_backend(self) -> str:
     # Canonicalize to turn into "cuda" or "rocm"
     return xb.canonicalize_platform(jax.default_backend())
 
+  def starter_data(self, inputs: Sequence[np.ndarray]) -> CompatTestData:
+    # Helper for starting a test, see module docstring.
+    assert isinstance(inputs, Sequence), f"{inputs}"
+    return dataclasses.replace(self.load_testdata(dummy_data_dict),
+                               inputs=inputs,
+                               platform=self.default_jax_backend())
+
   def load_testdata(self, testdata_dict: dict[str, Any]) -> CompatTestData:
     if testdata_dict["testdata_version"] == CURRENT_TESTDATA_VERSION:
       return CompatTestData(**testdata_dict)
@@ -212,7 +213,7 @@ def run_one_test(self, func: Callable[..., jax.Array],
     np.set_printoptions(threshold=sys.maxsize, floatmode="unique")
     # Print the current test data to simplify updating the test.
     updated_testdata = f"""
-# Pasted from the test output (see back_compat_test.py module docstring)
+# Pasted from the test output (see back_compat_test_util.py module docstring)
 data_{datetime.date.today().strftime('%Y_%m_%d')} = dict(
     testdata_version={CURRENT_TESTDATA_VERSION},
     platform={repr(self.default_jax_backend())},
diff --git a/jax/experimental/jax2tf/tests/back_compat_testdata/stablehlo_dynamic_top_k.py b/jax/experimental/jax2tf/tests/back_compat_testdata/stablehlo_dynamic_top_k.py
new file mode 100644
index 000000000000..ce4c3151a2ff
--- /dev/null
+++ b/jax/experimental/jax2tf/tests/back_compat_testdata/stablehlo_dynamic_top_k.py
@@ -0,0 +1,67 @@
+# Copyright 2023 The JAX Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# flake8: noqa
+
+import datetime
+from numpy import array, float32, int32
+
+
+# Pasted from the test output (see back_compat_test_util.py module docstring)
+data_2023_07_16 = dict(
+    testdata_version=1,
+    platform='cpu',
+    custom_call_targets=['stablehlo.dynamic_top_k'],
+    serialized_date=datetime.date(2023, 7, 16),
+    inputs=(array([[ 0.,  1.,  2.],
+       [ 3.,  4.,  5.],
+       [ 6.,  7.,  8.],
+       [ 9., 10., 11.]], dtype=float32),),
+    expected_outputs=(array([[ 2.,  1.],
+       [ 5.,  4.],
+       [ 8.,  7.],
+       [11., 10.]], dtype=float32), array([[2, 1],
+       [2, 1],
+       [2, 1],
+       [2, 1]], dtype=int32)),
+    mlir_module_text=r"""
+#loc = loc(unknown)
+module @jit_func attributes {mhlo.num_partitions = 1 : i32, mhlo.num_replicas = 1 : i32} {
+  func.func public @main(%arg0: tensor<4x?xf32> {jax.arg_info = "a", mhlo.sharding = "{replicated}"} loc(unknown)) -> (tensor<4x?xf32> {jax.result_info = "[0]"}, tensor<4x?xi32> {jax.result_info = "[1]"}) {
+    %0 = stablehlo.get_dimension_size %arg0, dim = 1 : (tensor<4x?xf32>) -> tensor<i32> loc(#loc3)
+    %1 = stablehlo.convert %0 : (tensor<i32>) -> tensor<i64> loc(#loc3)
+    %2 = stablehlo.constant dense<> : tensor<0xi1> loc(#loc)
+    %3 = stablehlo.convert %arg0 : tensor<4x?xf32> loc(#loc)
+    %4:2 = call @_wrapped_jax_export_main(%1, %3) : (tensor<i64>, tensor<4x?xf32>) -> (tensor<4x?xf32>, tensor<4x?xi32>) loc(#loc)
+    return %4#0, %4#1 : tensor<4x?xf32>, tensor<4x?xi32> loc(#loc)
+  } loc(#loc)
+  func.func private @_wrapped_jax_export_main(%arg0: tensor<i64> loc(unknown), %arg1: tensor<4x?xf32> {jax.arg_info = "a", mhlo.sharding = "{replicated}"} loc(unknown)) -> (tensor<4x?xf32> {jax.result_info = "[0]"}, tensor<4x?xi32> {jax.result_info = "[1]"}) {
+    %0 = stablehlo.convert %arg0 : tensor<i64> loc(#loc4)
+    %1 = stablehlo.constant dense<-1> : tensor<i64> loc(#loc5)
+    %2 = stablehlo.add %0, %1 : tensor<i64> loc(#loc6)
+    %3 = stablehlo.convert %2 : (tensor<i64>) -> tensor<i32> loc(#loc5)
+    %4:2 = stablehlo.custom_call @stablehlo.dynamic_top_k(%arg1, %3) {api_version = 2 : i32} : (tensor<4x?xf32>, tensor<i32>) -> (tensor<4x?xf32>, tensor<4x?xi32>) loc(#loc5)
+    return %4#0, %4#1 : tensor<4x?xf32>, tensor<4x?xi32> loc(#loc)
+  } loc(#loc)
+} loc(#loc)
+#loc1 = loc("third_party/py/jax/experimental/jax2tf/tests/back_compat_test.py":621:0)
+#loc2 = loc("third_party/py/jax/experimental/jax2tf/tests/back_compat_test.py":613:0)
+#loc3 = loc("/dimension_size[dimension=1]"(#loc1))
+#loc4 = loc("jit(func)/jit(main)/convert_element_type[new_dtype=int64 weak_type=False]"(#loc2))
+#loc5 = loc("jit(func)/jit(main)/top_k[k=b + -1]"(#loc2))
+#loc6 = loc("jit(func)/jit(main)/add"(#loc2))
+""",
+    mlir_module_serialized=b"ML\xefR\x01StableHLO_v0.9.0\x00\x01!\x05\x01\x03\x01\x03\x05\x03\x11\x07\t\x0b\r\x0f\x11\x13\x15\x03\xb5\x89\x19\x01Q\x07\x0b\x17\x0f\x0f\x0b\x0b\x0b\x0b\x0b\x0b\x0f#\x0b\x0b\x0b33\x0f\x0b\x13\x0b\x0f\x0bK\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x13\x0b\x0b\x17\x13\x13\x0b\x039\x0b\x1b\x13\x0b\x0b\x0f\x0b\x0b\x0b\x0b\x0b\x13\x0b\x13\x0b\x0b\x0b\x13\x0b\x0b\x0b/\x0b\x0b\x0b\x0b\x0f\x0f\x01\x03\x0f\x03\x177\x0f7\x07\x07\x0f\x13\x1b\x07\x1f\x07\x02R\x04\x1f\x05\x17\x17\x13\x96\t\x01\x1d+\x05\x11\x01\x05\x05\x19\x05\x1b\x05\x1d\x05\x1f\x05!\x05#\x1dGI\x03\x07\x1b\t\x1d\t\x03\x1f\x05%\x05'\x05)\x03\x0b\x0b[\re\x0fU\x03o\x11q\x03\x0b\x0bs\rw\x0fU\x03Y\x11y\x1d'\x05\x05+\x03\x03\x15{\x05-\x1d/\x05\x05/\x03\x113}5\x7f7\x819Q;\x83=Q?QAQ\x051\x053\x055\x057\x059\x05;\x05=\x05?\x03\x03E\x85\x05A\x05C\x17\x13\xb6\t\x01\x03\x03\x15\x87\x03\x03OY\x05E\x03\x01\r\x05]_ac\x03\x05gk\x1dG\x1dI\x03\x03S\x1dK\x1dM\x1dO\x1dQ#\x11\r\x03Wi\x1dS\r\x03Wm\x1dU\x1dW\x1dY\x03\x05uS\r\x01#\x15\x1d[\x1f\x05\x11\xff\xff\xff\xff\xff\xff\xff\xff\x0b\x05\x1d]\x1d_\x05\x01\x13\x0b\x05\x1f\x0f\x01\x01\x02\x02)\x05\x11\x00\xff\xff\xff\xff\xff\xff\xff\xff\x13)\x01\x0b)\x05\x11\x00\xff\xff\xff\xff\xff\xff\xff\xff\t\x1b\x1d)\x01\t)\x03\x01\x17\x11\x03\x03\x05\x03\x07\t\x11\x05\x05\x03\x05\x03\x07\x01\x04\xf3\x05\x01\x11\x01\x19\x07\x03\x01\t\x05\x11\x01!\x05\x03\x0f\x1b\x03\x03\x01\x0f\x07\x17C\x03\r\x03\x01\x03\x06\x17\x03\x05\x03\x03\x07\x03\x01K\x03\x0f\x03\x06\x01\x03\x03\x03\x01\x11\x07\x01M\x05\x03\x07\x05\x05\t\t\x04\x01\x05\x0b\r\x05\x11\x01#\x05\x03\x11\x1b\x05\x05\x01\x03\x01\x03\x06%\x03\x05\x03\x01\x07\x03\x07)\x03\x05\x0b\x06-\x03\x05\x05\x05\x07\x03\x06\x07\x03\r\x03\t\r\x07\x071\x05\x03\x07\x05\x03\x0b\t\x04\x01\x05\r\x0f\x06\x03\x01\x05\x01\x00R\x0ca1\x03\x11\x0f\x0b\t\t\x1b\x1d\x05\x1b3!\x0f;\x15\x1f/!!)#\x1f\x191I\x95\x13%)\r\x83\x1f\x15\x1d\x15\x13\x11-\x1f\x0f\x15\x19\x11\x17\x0f\x0b\x11builtin\x00vhlo\x00module\x00convert_v1\x00func_v1\x00constant_v1\x00return_v1\x00add_v1\x00custom_call_v1\x00get_dimension_size_v1\x00call_v1\x00sym_name\x00arg_attrs\x00function_type\x00res_attrs\x00sym_visibility\x00third_party/py/jax/experimental/jax2tf/tests/back_compat_test.py\x00value\x00mhlo.num_partitions\x00mhlo.num_replicas\x00jit_func\x00jit(func)/jit(main)/convert_element_type[new_dtype=int64 weak_type=False]\x00jit(func)/jit(main)/top_k[k=b + -1]\x00jit(func)/jit(main)/add\x00api_version\x00backend_config\x00call_target_name\x00called_computations\x00has_side_effect\x00operand_layouts\x00output_operand_aliases\x00result_layouts\x00dimension\x00/dimension_size[dimension=1]\x00callee\x00jax.result_info\x00_wrapped_jax_export_main\x00jax.arg_info\x00a\x00mhlo.sharding\x00{replicated}\x00[0]\x00[1]\x00main\x00public\x00private\x00\x00stablehlo.dynamic_top_k\x00",
+    xla_call_module_version=6,
+)  # End paste
diff --git a/jax/experimental/jax2tf/tests/shape_poly_test.py b/jax/experimental/jax2tf/tests/shape_poly_test.py
index 59fed2b5d107..80c737f59cd8 100644
--- a/jax/experimental/jax2tf/tests/shape_poly_test.py
+++ b/jax/experimental/jax2tf/tests/shape_poly_test.py
@@ -3097,10 +3097,6 @@ def test_harness(self, harness: PolyHarness):
         raise unittest.SkipTest(
             "native lowering with shape polymorphism requires additional StableHLO feature support")
 
-      if "top_k" in harness.fullname and "approx_top_k" not in harness.fullname:
-        # https://github.com/openxla/stablehlo/issues/1255: need DynamicTopK
-        raise unittest.SkipTest("native lowering with shape polymorphism not implemented for top_k")
-
       # Some tests need the latest jaxlib
       need_new_jaxlib = []
       if jaxlib_version < (0, 4, 13):