diff --git a/GPy/inference/latent_function_inference/inferenceX.py b/GPy/inference/latent_function_inference/inferenceX.py
index 949562ee..25d8d799 100644
--- a/GPy/inference/latent_function_inference/inferenceX.py
+++ b/GPy/inference/latent_function_inference/inferenceX.py
@@ -34,10 +34,11 @@ class InferenceX(Model):
     :type Y: numpy.ndarray
     """
     def __init__(self, model, Y, name='inferenceX', init='L2'):
-        if np.isnan(Y).any():
+        if np.isnan(Y).any() or getattr(model, 'missing_data', False):
             assert Y.shape[0]==1, "The current implementation of inference X only support one data point at a time with missing data!"
             self.missing_data = True
             self.valid_dim = np.logical_not(np.isnan(Y[0]))
+            self.ninan = getattr(model, 'ninan', None)
         else:
             self.missing_data = False
         super(InferenceX, self).__init__(name)
@@ -109,7 +110,10 @@ class InferenceX(Model):
         if self.missing_data:
             wv = wv[:,self.valid_dim]
             output_dim = self.valid_dim.sum()
-            self.dL_dpsi2 = beta*(output_dim*self.posterior.woodbury_inv - np.einsum('md,od->mo',wv, wv))/2.
+            if self.ninan is not None:
+                self.dL_dpsi2 = beta/2.*(self.posterior.woodbury_inv[:,:,self.valid_dim] - np.einsum('md,od->mo',wv, wv)[:, :, None]).sum(-1)
+            else:
+                self.dL_dpsi2 = beta/2.*(output_dim*self.posterior.woodbury_inv - np.einsum('md,od->mo',wv, wv))
             self.dL_dpsi1 = beta*np.dot(self.Y[:,self.valid_dim], wv.T)
             self.dL_dpsi0 = - beta/2.* np.ones(self.Y.shape[0])
         else: