diff --git a/tests/lax_scipy_sparse_test.py b/tests/lax_scipy_sparse_test.py
index ab55eb5a7..565639f91 100644
--- a/tests/lax_scipy_sparse_test.py
+++ b/tests/lax_scipy_sparse_test.py
@@ -313,9 +313,10 @@ class LaxBackedScipyTests(jtu.JaxTestCase):
     tol = shape[0] * jnp.finfo(dtype).eps
     x, info = jax.scipy.sparse.linalg._gmres(A_mv, b, tol=tol, atol=tol,
                                              restart=restart,
-                                             M=M,
-                                             qr_mode=qr_mode)
-    self.assertAllClose(x, solution, atol=300*jnp.finfo(x.dtype).eps)
+                                             M=M, qr_mode=qr_mode)
+    using_x64 = solution.dtype.kind in {np.float64, np.complex128}
+    solution_tol = 1e-8 if using_x64 else 1e-4
+    self.assertAllClose(x, solution, atol=solution_tol, rtol=solution_tol)
 
   @parameterized.named_parameters(jtu.cases_from_list(
       {"testcase_name":
@@ -345,10 +346,10 @@ class LaxBackedScipyTests(jtu.JaxTestCase):
     restart = shape[-1]
     tol = shape[0] * jnp.finfo(A.dtype).eps
     x, info = jax.scipy.sparse.linalg._gmres(A_mv, b, tol=tol, atol=tol,
-                                            restart=restart,
-                                            M=M,
-                                            qr_mode=qr_mode)
-    solution_tol = 300*jnp.finfo(x.dtype).eps
+                                             restart=restart,
+                                             M=M, qr_mode=qr_mode)
+    using_x64 = solution.dtype.kind in {np.float64, np.complex128}
+    solution_tol = 1e-8 if using_x64 else 1e-4
     self.assertAllClose(x, solution, atol=solution_tol, rtol=solution_tol)
 
   def test_gmres_pytree(self):