diff --git a/tests/linalg_test.py b/tests/linalg_test.py
index e687d4edbbd1..2a64b95b9452 100644
--- a/tests/linalg_test.py
+++ b/tests/linalg_test.py
@@ -909,7 +909,7 @@ def f(x):
       if dtype == np.complex128:
         atol = 2e-13
       else:
-        atol = 5e-4
+        atol = 6e-4
       self.assertArraysAllClose(t_out, b.real, atol=atol)
 
   def testJspSVDBasic(self):
diff --git a/tests/svd_test.py b/tests/svd_test.py
index 52833b4349ab..b349c3ca6eee 100644
--- a/tests/svd_test.py
+++ b/tests/svd_test.py
@@ -167,7 +167,7 @@ def testSvdWithOnRankDeficientInputZeroColumns(self, m, r):
       np.testing.assert_almost_equal(diff, 1e-4, decimal=2)
       # Check that u and v are orthogonal.
       self.assertAllClose(u.T.conj() @ u, np.eye(m), atol=10 * _SVD_TEST_EPS)
-      self.assertAllClose(v.T.conj() @ v, np.eye(m), atol=10 * _SVD_TEST_EPS)
+      self.assertAllClose(v.T.conj() @ v, np.eye(m), atol=11 * _SVD_TEST_EPS)
 
   @jtu.sample_product(
     [dict(m=m, n=n) for m, n in zip([2, 8, 10, 20], [4, 6, 10, 18])],