diff --git a/GPy/testing/model_tests.py b/GPy/testing/model_tests.py
index c0316cf1..144c6adf 100644
--- a/GPy/testing/model_tests.py
+++ b/GPy/testing/model_tests.py
@@ -301,11 +301,20 @@ class MiscTests(unittest.TestCase):
 
         warp_k = GPy.kern.RBF(1)
         warp_f = GPy.util.warping_functions.IdentityFunction(closed_inverse=False)
-        warp_m = GPy.models.WarpedGP(self.X, self.Y, kernel=warp_k, warping_function=warp_f)
+        warp_m = GPy.models.WarpedGP(self.X, self.Y, kernel=warp_k, 
+                                     warping_function=warp_f)
         warp_m.optimize()
         warp_preds = warp_m.predict(self.X)
+
+        warp_k_exact = GPy.kern.RBF(1)
+        warp_f_exact = GPy.util.warping_functions.IdentityFunction()
+        warp_m_exact = GPy.models.WarpedGP(self.X, self.Y, kernel=warp_k_exact, 
+                                           warping_function=warp_f_exact)
+        warp_m_exact.optimize()
+        warp_preds_exact = warp_m_exact.predict(self.X)
  
         np.testing.assert_almost_equal(preds, warp_preds, decimal=4)
+        np.testing.assert_almost_equal(preds, warp_preds_exact, decimal=4)
 
     def test_warped_gp_log(self):
         """
@@ -322,11 +331,20 @@ class MiscTests(unittest.TestCase):
 
         warp_k = GPy.kern.RBF(1)
         warp_f = GPy.util.warping_functions.LogFunction(closed_inverse=False)
-        warp_m = GPy.models.WarpedGP(self.X, Y, kernel=warp_k, warping_function=warp_f)
+        warp_m = GPy.models.WarpedGP(self.X, Y, kernel=warp_k, 
+                                     warping_function=warp_f)
         warp_m.optimize()
         warp_preds = warp_m.predict(self.X, median=True)[0]
+
+        warp_k_exact = GPy.kern.RBF(1)
+        warp_f_exact = GPy.util.warping_functions.LogFunction()
+        warp_m_exact = GPy.models.WarpedGP(self.X, Y, kernel=warp_k_exact, 
+                                           warping_function=warp_f_exact)
+        warp_m_exact.optimize(messages=True)
+        warp_preds_exact = warp_m_exact.predict(self.X, median=True)[0]
  
         np.testing.assert_almost_equal(np.exp(preds), warp_preds, decimal=4)
+        np.testing.assert_almost_equal(np.exp(preds), warp_preds_exact, decimal=4)
 
     def test_warped_gp_cubic_sine(self, max_iters=100):
         """