diff --git a/GPy/testing/gpy_kernels_state_space_tests.py b/GPy/testing/gpy_kernels_state_space_tests.py
index 785ae92f..034b58bb 100644
--- a/GPy/testing/gpy_kernels_state_space_tests.py
+++ b/GPy/testing/gpy_kernels_state_space_tests.py
@@ -28,23 +28,22 @@ class StateSpaceKernelsTests(np.testing.TestCase):
                                 kalman_filter_type=kalman_filter_type,
                                 use_cython=use_cython)
 
+        m1.likelihood[:] = Y.var()/10.
+
         if check_gradients:
             self.assertTrue(m1.checkgrad())
 
         if 1:#optimize:
-            m1.optimize(optimizer='lbfgsb',max_iters=2)
+            m1.optimize(optimizer='lbfgsb', max_iters=1)
 
         if compare_with_GP and (predict_X is None):
             predict_X = X
 
         self.assertTrue(compare_with_GP)
         if compare_with_GP:
-            np.random.seed(254856)
             m2  = GPy.models.GPRegression(X,Y, gp_kernel)
-            #m2.randomize()
-            m2.optimize(max_iters=optimize_max_iters)
 
-            m1[:] = m2[:]
+            m2[:] = m1[:]
 
             if (predict_X is not None):
                 x_pred_reg_1 = m1.predict(predict_X)
@@ -53,12 +52,12 @@ class StateSpaceKernelsTests(np.testing.TestCase):
             x_pred_reg_2 = m2.predict(predict_X)
             x_quant_reg_2 = m2.predict_quantiles(predict_X)
 
-            np.testing.assert_array_almost_equal(x_pred_reg_1[0], x_pred_reg_2[0], 3)
-            np.testing.assert_array_almost_equal(x_pred_reg_1[1], x_pred_reg_2[1], 3)
-            np.testing.assert_array_almost_equal(x_quant_reg_1[0], x_quant_reg_2[0], 3)
-            np.testing.assert_array_almost_equal(x_quant_reg_1[1], x_quant_reg_2[1], 3)
-            np.testing.assert_almost_equal(m1.log_likelihood(), m2.log_likelihood(), 3)
-            np.testing.assert_array_almost_equal(m1.gradient, m2.gradient, 2)
+            np.testing.assert_array_almost_equal(x_pred_reg_1[0], x_pred_reg_2[0], mean_compare_decimal)
+            np.testing.assert_array_almost_equal(x_pred_reg_1[1], x_pred_reg_2[1], var_compare_decimal)
+            np.testing.assert_array_almost_equal(x_quant_reg_1[0], x_quant_reg_2[0], mean_compare_decimal)
+            np.testing.assert_array_almost_equal(x_quant_reg_1[1], x_quant_reg_2[1], mean_compare_decimal)
+            np.testing.assert_array_almost_equal(m1.gradient, m2.gradient, var_compare_decimal)
+            np.testing.assert_almost_equal(m1.log_likelihood(), m2.log_likelihood(), var_compare_decimal)
 
 
     def test_Matern32_kernel(self,):
@@ -103,7 +102,7 @@ class StateSpaceKernelsTests(np.testing.TestCase):
                            predict_X=X,
                            gp_kernel=gp_kernel,
                            optimize_max_iters=1000,
-                           mean_compare_decimal=2, var_compare_decimal=2)
+                           mean_compare_decimal=2, var_compare_decimal=1)
 
     def test_periodic_kernel(self,):
         np.random.seed(322) # seed the random number generator
@@ -172,7 +171,7 @@ class StateSpaceKernelsTests(np.testing.TestCase):
         self.run_for_model(X, Y, ss_kernel, check_gradients=True,
                             predict_X=X,
                             gp_kernel=gp_kernel,
-                            mean_compare_decimal=5, var_compare_decimal=5)
+                            mean_compare_decimal=4, var_compare_decimal=4)
 
     def test_exponential_kernel(self,):
         np.random.seed(12345) # seed the random number generator