diff --git a/GPy/core/gp.py b/GPy/core/gp.py
index 303921ea..9cbe3daf 100644
--- a/GPy/core/gp.py
+++ b/GPy/core/gp.py
@@ -377,7 +377,7 @@ class GP(Model):
         if full_cov:
             dK2_dXdX = kern.gradients_XX(one, Xnew)
         else:
-            dK2_dXdX = kern.gradients_XX(one, Xnew).sum(0)
+            dK2_dXdX = kern.gradients_XX_diag(one, Xnew)
             #dK2_dXdX = np.zeros((Xnew.shape[0], Xnew.shape[1], Xnew.shape[1]))
             #for i in range(Xnew.shape[0]):
             #    dK2_dXdX[i:i+1,:,:] = kern.gradients_XX(one, Xnew[i:i+1,:])
diff --git a/GPy/kern/src/integral.py b/GPy/kern/src/integral.py
index d2827390..971a48a8 100644
--- a/GPy/kern/src/integral.py
+++ b/GPy/kern/src/integral.py
@@ -10,10 +10,10 @@ class Integral(Kern): #todo do I need to inherit from Stationary
     """
     Integral kernel between...
     """
-    
+
     def __init__(self, input_dim, variances=None, lengthscale=None, ARD=False, active_dims=None, name='integral'):
         super(Integral, self).__init__(input_dim, active_dims, name)
-        
+
         if lengthscale is None:
             lengthscale = np.ones(1)
         else:
@@ -22,7 +22,7 @@ class Integral(Kern): #todo do I need to inherit from Stationary
         self.lengthscale = Param('lengthscale', lengthscale, Logexp()) #Logexp - transforms to allow positive only values...
         self.variances = Param('variances', variances, Logexp()) #and here.
         self.link_parameters(self.variances, self.lengthscale) #this just takes a list of parameters we need to optimise.
-    
+
     def h(self, z):
         return 0.5 * z * np.sqrt(math.pi) * math.erf(z) + np.exp(-(z**2))
 
@@ -36,13 +36,13 @@ class Integral(Kern): #todo do I need to inherit from Stationary
             for i,x in enumerate(X):
                 for j,x2 in enumerate(X):
                     dK_dl[i,j] = self.variances[0]*self.dk_dl(x[0],x2[0],self.lengthscale[0]) #TODO Multiple length scales
-                    dK_dv[i,j] = self.k_xx(x[0],x2[0],self.lengthscale[0])  #the gradient wrt the variance is k_xx.              
+                    dK_dv[i,j] = self.k_xx(x[0],x2[0],self.lengthscale[0])  #the gradient wrt the variance is k_xx.
             self.lengthscale.gradient = np.sum(dK_dl * dL_dK)
             self.variances.gradient = np.sum(dK_dv * dL_dK)
             #print "V%0.5f" % self.variances.gradient
             #print "L%0.5f" % self.lengthscale.gradient
-        else:     #we're finding dK_xf/Dtheta                
-            print "NEED TO HANDLE TODO!"
+        else:     #we're finding dK_xf/Dtheta
+            print("NEED TO HANDLE TODO!")
 
     #useful little function to help calculate the covariances.
     def g(self,z):
@@ -52,15 +52,15 @@ class Integral(Kern): #todo do I need to inherit from Stationary
     def k_xx(self,t,tprime,l):
         return 0.5 * (l**2) * ( self.g(t/l) - self.g((t - tprime)/l) + self.g(tprime/l) - 1)
 
-    def k_ff(self,t,tprime,l): 
+    def k_ff(self,t,tprime,l):
         return np.exp(-((t-tprime)**2)/(l**2)) #rbf
-        
+
     #covariance between the gradient and the actual value
     def k_xf(self,t,tprime,l):
         return 0.5 * np.sqrt(math.pi) * l * (math.erf((t-tprime)/l) + math.erf(tprime/l))
 
     def K(self, X, X2=None):
-        if X2 is None:         
+        if X2 is None:
             K_xx = np.zeros([X.shape[0],X.shape[0]])
             for i,x in enumerate(X):
                 for j,x2 in enumerate(X):
@@ -73,7 +73,7 @@ class Integral(Kern): #todo do I need to inherit from Stationary
                     K_xf[i,j] = self.k_xf(x[0],x2[0],self.lengthscale[0])
             #print self.variances[0]
             return K_xf * self.variances[0]
-            
+
     def Kdiag(self, X):
         """I've used the fact that we call this method for K_ff when finding the covariance as a hack so
         I know if I should return K_ff or K_xx. In this case we're returning K_ff!!
diff --git a/GPy/kern/src/stationary.py b/GPy/kern/src/stationary.py
index 3bf75a4b..1ce8084f 100644
--- a/GPy/kern/src/stationary.py
+++ b/GPy/kern/src/stationary.py
@@ -273,7 +273,7 @@ class Stationary(Kern):
             dL2_dXdX: [NxQxQ]
         """
         dL_dK_diag = dL_dK_diag.copy().reshape(-1, 1, 1)
-        assert dL_dK_diag.size == X.shape[0], "dL_dK_diag has to be given as row [N] or column vector [Nx1]"
+        assert (dL_dK_diag.size == X.shape[0]) or (dL_dK_diag.size == 1), "dL_dK_diag has to be given as row [N] or column vector [Nx1]"
 
         l4 =  np.ones(X.shape[1])*self.lengthscale**2
         return dL_dK_diag * (np.eye(X.shape[1]) * -self.dK2_drdr_diag()/(l4))[None, :,:]# np.zeros(X.shape+(X.shape[1],))