diff --git a/optax/_src/linesearch_test.py b/optax/_src/linesearch_test.py
index ab3a2dfd..ac11a692 100644
--- a/optax/_src/linesearch_test.py
+++ b/optax/_src/linesearch_test.py
@@ -485,8 +485,8 @@ def test_linesearch(self, problem_name: str, seed: int):
     with self.subTest('Check against scipy'):
       stepsize = otu.tree_get(final_state, 'learning_rate')
       final_value = otu.tree_get(final_state, 'value')
-      chex.assert_trees_all_close(scipy_res[0], stepsize, rtol=1e-5)
-      chex.assert_trees_all_close(scipy_res[3], final_value, rtol=1e-5)
+      chex.assert_trees_all_close(scipy_res[0], stepsize, rtol=1e-4)
+      chex.assert_trees_all_close(scipy_res[3], final_value, rtol=1e-4)
 
   def test_failure_descent_direction(self):
     """Check failure when updates are not a descent direction."""
diff --git a/optax/perturbations/_make_pert_test.py b/optax/perturbations/_make_pert_test.py
index 7928fd37..44e2f792 100644
--- a/optax/perturbations/_make_pert_test.py
+++ b/optax/perturbations/_make_pert_test.py
@@ -114,7 +114,7 @@ def exact_loss(inputs):
     chex.assert_trees_all_close(expected_grad, got_grad, atol=2e-2)
     expected_dict = pert_argmax_fun(self.tree_a_dict_jax, self.rng_jax)
     got_dict = jtu.tree_map(softmax_fun, self.tree_a_dict_jax)
-    chex.assert_trees_all_close(expected_dict, got_dict, atol=2e-2)
+    chex.assert_trees_all_close(expected_dict, got_dict, atol=3e-2)
 
   def test_values_on_tree(self):
     """Test that the perturbations are well applied for functions on trees.