diff --git a/GPy/kern/bias.py b/GPy/kern/bias.py
index 6d1bbf3f..3cd78afa 100644
--- a/GPy/kern/bias.py
+++ b/GPy/kern/bias.py
@@ -9,10 +9,10 @@ import hashlib
 class bias(kernpart):
     def __init__(self,D,variance=1.):
         """
-        Arguments
-        ----------
-        D: int - the number of input dimensions
-        variance: float
+        :param D: the number of input dimensions
+        :type D: int
+        :param variance: the variance of the kernel
+        :type variance: float
         """
         self.D = D
         self.Nparam = 1
@@ -30,19 +30,16 @@ class bias(kernpart):
         return ['variance']
 
     def K(self,X,X2,target):
-        if X2 is None: X2 = X
-        np.add(self.variance, target,target)
+        target += self.variance
 
     def Kdiag(self,X,target):
-        np.add(target,self.variance,target)
+        target += self.variance
 
-    def dK_dtheta(self,X,X2,target):
-        """Return shape is NxMx(Ntheta)"""
-        if X2 is None: X2 = X
-        np.add(target[:,:,0],1., target[:,:,0])
+    def dK_dtheta(self,partial,X,X2,target):
+        target += partial.sum()
 
-    def dKdiag_dtheta(self,X,target):
-        np.add(target[:,0],1.,target[:,0])
+    def dKdiag_dtheta(self,partial,X,target):
+        target += partial.sum()
 
     def dK_dX(self, X, X2, target):
         pass
diff --git a/GPy/kern/linear.py b/GPy/kern/linear.py
index 9470d29a..8f960a9c 100644
--- a/GPy/kern/linear.py
+++ b/GPy/kern/linear.py
@@ -37,20 +37,16 @@ class linear(kernpart):
     def Kdiag(self,X,target):
         np.add(target,np.sum(self.variance*np.square(X),-1),target)
 
-    def dK_dtheta(self,X,X2,target):
+    def dK_dtheta(self,partial,X,X2,target):
         """
         Computes the derivatives wrt theta
         Return shape is NxMx(Ntheta)
-
         """
+        product = np.dot(X, X2.T)
+        target += np.sum(product*partial)
 
-        if X2 is None: X2 = X
-        product = np.dot(X, X2.T)[:,:, None]#X[:,None,:]*X2[None,:,:]
-        target += product
-
-    def dK_dX(self,X,X2,target):
-        if X2 is None: X2 = X
-        np.add(target,X2[:,None,:]*self.variance,target)
+    def dK_dX(self,partial,X,X2,target):
+        target += self.variance * np.sum(partial[:,None,:]*X2.T[None,:,:],-1)
 
     # def psi0(self,Z,mu,S,target):
     #     expected = np.square(mu) + S
diff --git a/GPy/kern/rbf.py b/GPy/kern/rbf.py
index 087285d1..f899737a 100644
--- a/GPy/kern/rbf.py
+++ b/GPy/kern/rbf.py
@@ -63,7 +63,7 @@ class rbf(kernpart):
         self._K_computations(X,X2)
         _K_dist = X[:,None,:]-X2[None,:,:]
         dK_dX = np.transpose(-self.variance*self._K_dvar[:,:,np.newaxis]*_K_dist/self.lengthscale2,(1,0,2))
-        target += np.sum(dK_dX*partial[:,:,None],1)
+        target += np.sum(dK_dX*partial[:,:,None],0)
 
     def dKdiag_dX(self,X,target):
         pass
diff --git a/GPy/kern/white.py b/GPy/kern/white.py
index beb99416..04effabc 100644
--- a/GPy/kern/white.py
+++ b/GPy/kern/white.py
@@ -15,7 +15,7 @@ class white(kernpart):
     """
     def __init__(self,D,variance=1.):
         self.D = D
-        self.Nparam = 1.
+        self.Nparam = 1
         self.name = 'white'
         self.set_param(np.array([variance]).flatten())
 
diff --git a/GPy/models/GP_regression.py b/GPy/models/GP_regression.py
index b6959448..c766f017 100644
--- a/GPy/models/GP_regression.py
+++ b/GPy/models/GP_regression.py
@@ -29,7 +29,7 @@ class GP_regression(model):
 
     def __init__(self,X,Y,kernel=None,normalize_X=False,normalize_Y=False, Xslices=None):
         if kernel is None:
-            kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1])
+            kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1]) + kern.bias(X.shape[1])
 
         # parse arguments
         self.Xslices = Xslices