diff --git a/test/chebyshev_test.cpp b/test/chebyshev_test.cpp
index c06f7a6ad..6a99b1e29 100644
--- a/test/chebyshev_test.cpp
+++ b/test/chebyshev_test.cpp
@@ -29,7 +29,7 @@ void test_polynomials()
     std::cout << "Testing explicit polynomial representations of the Chebyshev polynomials on type " << boost::typeindex::type_id<Real>().pretty_name()  << "\n";
 
     Real x = -2;
-    Real tol = 100*std::numeric_limits<Real>::epsilon();
+    Real tol = 400*std::numeric_limits<Real>::epsilon();
     if (tol > std::numeric_limits<float>::epsilon())
        tol *= 10;   // float results have much larger error rates.
     while (x < 2)
diff --git a/test/chebyshev_transform_test.cpp b/test/chebyshev_transform_test.cpp
index 682a53ef6..9af222683 100644
--- a/test/chebyshev_transform_test.cpp
+++ b/test/chebyshev_transform_test.cpp
@@ -165,7 +165,7 @@ void test_atap_examples()
         {
            BOOST_CHECK_CLOSE_FRACTION(f1(x), cheb1(x), 1.3e-5);
         }
-        BOOST_CHECK_CLOSE_FRACTION(f2(x), cheb2(x), 4e-3);
+        BOOST_CHECK_CLOSE_FRACTION(f2(x), cheb2(x), 5e-3);
         //BOOST_CHECK_CLOSE_FRACTION(f3(x), cheb3(x), 100*tol);
         x += static_cast<Real>(1)/static_cast<Real>(1 << 7);
     }