diff --git a/pyscf/hessian/test/test_uks.py b/pyscf/hessian/test/test_uks.py
index 98e9381fa5..b7e5b93513 100644
--- a/pyscf/hessian/test/test_uks.py
+++ b/pyscf/hessian/test/test_uks.py
@@ -115,8 +115,9 @@ def test_finite_diff_b3lyp_hess(self):
         mf.conv_tol = 1e-14
         mf.xc = 'b3lyp5'
         e0 = mf.kernel()
+        mf.conv_tol_cpscf = 1e-9
         hess = mf.Hessian().kernel()
-        self.assertAlmostEqual(lib.fp(hess), -0.8208641727673912, 6)
+        self.assertAlmostEqual(lib.fp(hess), -0.8208641727673912, 5)
 
         g_scanner = mf.nuc_grad_method().as_scanner()
         pmol = mol.copy()
diff --git a/pyscf/lib/test/test_linalg_helper.py b/pyscf/lib/test/test_linalg_helper.py
index 1d71a5f6d7..158938f606 100644
--- a/pyscf/lib/test/test_linalg_helper.py
+++ b/pyscf/lib/test/test_linalg_helper.py
@@ -135,7 +135,7 @@ def test_krylov_multiple_roots(self):
         ref = numpy.linalg.solve(numpy.eye(n) + a, b.T).T
 
         aop = lambda x: x.dot(a.T)
-        c = linalg_helper.krylov(aop, b)
+        c = linalg_helper.krylov(aop, b, lindep=1e-14)
         self.assertAlmostEqual(abs(ref - c).max(), 0, 7)
 
         a = numpy.random.rand(n,n) * .1 + numpy.random.rand(n,n) * .1j
@@ -143,7 +143,7 @@ def test_krylov_multiple_roots(self):
         ref = numpy.linalg.solve(numpy.eye(n) + a, b.T).T
 
         aop = lambda x: x.dot(a.T)
-        c = linalg_helper.krylov(aop, b)
+        c = linalg_helper.krylov(aop, b, lindep=1e-14)
         self.assertAlmostEqual(abs(ref - c).max(), 0, 7)
 
     def test_dgeev(self):