diff --git a/tests/test_spline_utils.py b/tests/test_spline_utils.py
index 1d701d13..aa6834a1 100644
--- a/tests/test_spline_utils.py
+++ b/tests/test_spline_utils.py
@@ -620,7 +620,7 @@ def test_pspline_lam_extremes(data_fixture, diff_order, allow_lower, spline_degr
         # and both larger num_knots and larger diff_orders need larger lam for it to be a
         # polynomial, so have to reduce the relative tolerance; num_knots has a larger effect
         # than diff_order, so base the rtol on it
-        rtol = {50: 5e-4, 501: 5e-3}[num_knots]
+        rtol = {50: 1e-3, 501: 5e-3}[num_knots]
         assert_allclose(output, polynomial_fit, rtol=rtol, atol=1e-10)
 
     # for lam ~ 0, should just approximate the an interpolating spline
diff --git a/tests/test_whittaker.py b/tests/test_whittaker.py
index e77f1e82..ef50f281 100644
--- a/tests/test_whittaker.py
+++ b/tests/test_whittaker.py
@@ -324,7 +324,7 @@ def test_sparse_comparison(self, diff_order, eta):
             self.y, lam=lam, eta=eta, diff_order=diff_order, max_iter=max_iter, tol=tol
         )
 
-        assert_allclose(banded_output, sparse_output, rtol=1e-6, atol=1e-10)
+        assert_allclose(banded_output, sparse_output, rtol=1.5e-6, atol=1e-10)
 
 
 class TestIArPLS(WhittakerTester):
@@ -445,7 +445,7 @@ def test_sparse_comparison(self, diff_order, asymmetric_coef):
             asymmetric_coef=asymmetric_coef
         )[0]
 
-        rtol = {2: 1e-4, 3: 2e-4}[diff_order]
+        rtol = {2: 1.5e-4, 3: 3e-4}[diff_order]
         assert_allclose(banded_output, sparse_output, rtol=rtol, atol=1e-8)