diff --git a/tests/export_test.py b/tests/export_test.py
index 0d87d0c52d36..4ad0f5f50699 100644
--- a/tests/export_test.py
+++ b/tests/export_test.py
@@ -946,22 +946,22 @@ def f_jax_inner(x):
 
     exp = export.export(f_jax)(x)
     if exp.serialization_version >= export._VERSION_START_SUPPORT_EFFECTS_WITH_REAL_TOKENS:
-      self.assertSetEqual({"TestingOrderedEffect1", "TestingOrderedEffect2"},
-                          {str(e) for e in exp.ordered_effects})
-      self.assertEqual({"TestingUnorderedEffect1"},
-                       {str(e) for e in exp.unordered_effects})
+      self.assertEqual(["TestingOrderedEffect1", "TestingOrderedEffect2"],
+                       sorted(str(e) for e in exp.ordered_effects))
+      self.assertEqual(["TestingUnorderedEffect1"],
+                       [str(e) for e in exp.unordered_effects])
     else:
-      self.assertSetEqual(set(), {str(e) for e in exp.ordered_effects})
-      self.assertSetEqual(set(), {str(e) for e in exp.unordered_effects})
+      self.assertEqual([], [str(e) for e in exp.ordered_effects])
+      self.assertEqual([], [str(e) for e in exp.unordered_effects])
     mlir_module_str = str(exp.mlir_module())
 
     # Inner functions use stablehlo.token for all versions
     inner_fun_expected_re = (
       r"func.func private @f_jax_inner\("
-      r"%arg0: !stablehlo.token {jax.token = true}.*"
+      r"%arg0: !stablehlo.token .*jax.token = true.*"
       r"%arg1: tensor<3xf32>.*->.*"
       # Results
-      r"!stablehlo.token {jax.token = true}.*"
+      r"!stablehlo.token .*jax.token = true.*"
       r"tensor<3xf32>"
     )
     self.assertRegex(mlir_module_str, inner_fun_expected_re)
@@ -970,11 +970,11 @@ def f_jax_inner(x):
     # i1[0] before version 9.
     wrapped_main_expected_re = (
       r"@_wrapped_jax_export_main\("
-      r"%arg0: !stablehlo.token {jax.token = true}.*"
-      r"%arg1: !stablehlo.token {jax.token = true}.*->.*"
+      r"%arg0: !stablehlo.token .*jax.token = true.*"
+      r"%arg1: !stablehlo.token .*jax.token = true.*->.*"
       # Results
-      r"!stablehlo.token {jax.token = true}.*"
-      r"!stablehlo.token {jax.token = true}.*")
+      r"!stablehlo.token .*jax.token = true.*"
+      r"!stablehlo.token .*jax.token = true.*")
     if exp.serialization_version < export._VERSION_START_SUPPORT_EFFECTS_WITH_REAL_TOKENS:
       wrapped_main_expected_re = wrapped_main_expected_re.replace("!stablehlo.token", "tensor<0xi1>")
     self.assertRegex(mlir_module_str, wrapped_main_expected_re)
@@ -987,20 +987,32 @@ def f_jax_inner(x):
       main_expected_re = wrapped_main_expected_re.replace("@_wrapped_jax_export_main", "@main")
       self.assertRegex(mlir_module_str, main_expected_re)
 
-    lowered = jax.jit(export.call_exported(exp)).lower(x)
+    # Now call the exported from a function that uses its own effects
+    def f_outer(x):
+      return (
+        testing_primitive_with_effect_p.bind(
+          x, effect_class_name="TestingOrderedEffect2") +
+        testing_primitive_with_effect_p.bind(
+          x, effect_class_name="TestingUnorderedEffect1") +
+        export.call_exported(exp)(x))
+
+    lowered_outer = jax.jit(f_outer).lower(x)
     if exp.serialization_version < export._VERSION_START_SUPPORT_EFFECTS_WITH_REAL_TOKENS:
-      self.assertSetEqual(set(),
-                          {str(e) for e in lowered._lowering.compile_args["ordered_effects"]})
-      self.assertSetEqual(set(),
-                          {str(e) for e in lowered._lowering.compile_args["unordered_effects"]})
+      self.assertEqual(["TestingOrderedEffect2"],
+                       [str(e) for e in lowered_outer._lowering.compile_args["ordered_effects"]])
     else:
-      self.assertSetEqual({"TestingOrderedEffect1", "TestingOrderedEffect2"},
-                          {str(e) for e in lowered._lowering.compile_args["ordered_effects"]})
-      self.assertSetEqual({"TestingUnorderedEffect1"},
-                          {str(e) for e in lowered._lowering.compile_args["unordered_effects"]})
+      self.assertEqual(["TestingOrderedEffect1", "TestingOrderedEffect2"],
+                       sorted(str(e) for e in lowered_outer._lowering.compile_args["ordered_effects"]))
+    self.assertEqual(["TestingUnorderedEffect1"],
+                     sorted([str(e) for e in lowered_outer._lowering.compile_args["unordered_effects"]]))
 
-    res = export.call_exported(exp)(x)
-    self.assertAllClose(10. + 4. * 2. * x, res)
+    mlir_outer_module_str = str(lowered_outer.compiler_ir())
+    if exp.serialization_version >= export._VERSION_START_SUPPORT_EFFECTS_WITH_REAL_TOKENS:
+      main_expected_re = main_expected_re.replace("!stablehlo.token", "tensor<0xi1>")
+      self.assertRegex(mlir_outer_module_str, main_expected_re)
+
+    res = jax.jit(f_outer)(x)
+    self.assertAllClose(2. * 2. * x + 10. + 4. * 2. * x, res)
 
   @jtu.parameterized_filterable(
     kwargs=[