diff --git a/GPy/examples/sparse_GP_regression_demo.py b/GPy/examples/sparse_GP_regression_demo.py
index 6424b8f2..d67a3831 100644
--- a/GPy/examples/sparse_GP_regression_demo.py
+++ b/GPy/examples/sparse_GP_regression_demo.py
@@ -11,8 +11,8 @@ import numpy as np
 import GPy
 np.random.seed(2)
 pb.ion()
-N = 500
-M = 5
+N = 1200
+M = 20
 
 ######################################
 ## 1 dimensional example
@@ -27,20 +27,21 @@ noise = GPy.kern.white(1)
 kernel = rbf + noise
 
 # create simple GP model
-m1 = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
+m = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
 
 # contrain all parameters to be positive
-m1.constrain_positive('(variance|lengthscale|precision)')
-#m1.constrain_positive('(variance|lengthscale)')
-#m1.constrain_fixed('prec',10.)
+m.constrain_positive('(variance|lengthscale|precision)')
+#m.constrain_positive('(variance|lengthscale)')
+#m.constrain_fixed('prec',10.)
 
 
 #check gradient FIXME unit test please
-m1.checkgrad()
+m.checkgrad(verbose=1)
+stop
 # optimize and plot
-m1.optimize('tnc', messages = 1)
-m1.plot()
-# print(m1)
+m.optimize('tnc', messages = 1)
+m.plot()
+# print(m)
 
 ######################################
 ## 2 dimensional example
diff --git a/GPy/models/sparse_GP_regression.py b/GPy/models/sparse_GP_regression.py
index 6313f4f7..6d1b1f44 100644
--- a/GPy/models/sparse_GP_regression.py
+++ b/GPy/models/sparse_GP_regression.py
@@ -37,7 +37,7 @@ class sparse_GP_regression(GP_regression):
     """
 
     def __init__(self,X,Y,kernel=None, X_uncertainty=None, beta=100., Z=None,Zslices=None,M=10,normalize_X=False,normalize_Y=False):
-        self.stabilit_multiplier = 1.
+        self.scale_factor = 1e1
         self.beta = beta
         if Z is None:
             self.Z = np.random.permutation(X.copy())[:M]
@@ -60,14 +60,6 @@ class sparse_GP_regression(GP_regression):
         if self.has_uncertain_inputs:
             self.X_uncertainty /= np.square(self._Xstd)
 
-    def set_param(self, p):
-        self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
-        self.beta = p[self.M*self.Q]
-        self.kern.set_param(p[self.Z.size + 1:])
-        self.beta2 = self.beta**2
-        self._compute_kernel_matrices()
-        self._computations()
-
     def _compute_kernel_matrices(self):
         # kernel computations, using BGPLVM notation
         #TODO: slices for psi statistics (easy enough)
@@ -77,35 +69,62 @@ class sparse_GP_regression(GP_regression):
             self.psi0 = self.kern.psi0(self.Z,self.X, self.X_uncertainty).sum()
             self.psi1 = self.kern.psi1(self.Z,self.X, self.X_uncertainty).T
             self.psi2 = self.kern.psi2(self.Z,self.X, self.X_uncertainty)
+            raise NotImplementedError, "scale psi2 (in kern?)"
         else:
             self.psi0 = self.kern.Kdiag(self.X,slices=self.Xslices).sum()
             self.psi1 = self.kern.K(self.Z,self.X)
-            self.psi2 = np.dot(self.psi1,self.psi1.T)
+            #self.psi2 = np.dot(self.psi1,self.psi1.T)
+            #self.psi2 = self.psi1.T[:,:,None]*self.psi1.T[:,None,:]
+            self.psi1_scaled = self.psi1/self.scale_factor
+            #self.psi2_scaled = psi1_scaled.T[:,:,None]*psi1_scaled.T[:,None,:]
+            self.psi2_scaled = np.dot(self.psi1_scaled,self.psi1_scaled.T)
 
     def _computations(self):
         # TODO find routine to multiply triangular matrices
-        self.V = self.beta*self.Y
+        sf = self.scale_factor
+        sf2 = sf**2
+
+        self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
+
+        self.V = (self.beta/self.scale_factor)*self.Y
+        self.A = mdot(self.Lmi, self.beta*self.psi2_scaled, self.Lmi.T)
+        self.B = np.eye(self.M)/sf2 + self.A
+
+        self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
+
         self.psi1V = np.dot(self.psi1, self.V)
         self.psi1VVpsi1 = np.dot(self.psi1V, self.psi1V.T)
-        self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
-        self.A = mdot(self.Lmi, self.beta*self.psi2, self.Lmi.T)
-        self.B = np.eye(self.M)*self.stabilit_multiplier + self.A
-        self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
-        self.LLambdai = np.dot(self.LBi, self.Lmi)
-        self.trace_K = self.psi0 - np.trace(self.A)/self.beta
-        self.LBL_inv = mdot(self.Lmi.T, self.Bi, self.Lmi)
-        self.C = mdot(self.LLambdai, self.psi1V)
-        self.G =  mdot(self.LBL_inv, self.psi1VVpsi1, self.LBL_inv.T)
+        self.C = mdot(self.Lmi.T, self.Bi, self.Lmi)
+        self.E = mdot(self.C, self.psi1VVpsi1/sf2, self.C.T)
 
         # Compute dL_dpsi
         self.dL_dpsi0 = - 0.5 * self.D * self.beta * np.ones(self.N)
-        self.dL_dpsi1 = mdot(self.LLambdai.T,self.C,self.V.T)
-        self.dL_dpsi2 = - 0.5 * self.beta * (self.D*(self.LBL_inv - self.Kmmi) + self.G)
+        self.dL_dpsi1 = mdot(self.V, self.psi1V.T,self.C).T
+        self.dL_dpsi2 = 0.5 * self.beta * self.D * self.Kmmi # dB
+        self.dL_dpsi2 += - 0.5 * self.beta/sf2 * self.D * self.C # dC
+        self.dL_dpsi2 += - 0.5 * self.beta * self.E # dD
 
         # Compute dL_dKmm
-        self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi) # dB
-        self.dL_dKmm += -0.5 * self.D * (- self.LBL_inv - 2.*self.beta*mdot(self.LBL_inv, self.psi2, self.Kmmi) + self.Kmmi) # dC
-        self.dL_dKmm +=  np.dot(np.dot(self.G,self.beta*self.psi2) - np.dot(self.LBL_inv, self.psi1VVpsi1), self.Kmmi) + 0.5*self.G # dE
+        self.dL_dKmm = -0.5 * self.D * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB
+        self.dL_dKmm += -0.5 * self.D * (- self.C/sf2 - 2.*self.beta*mdot(self.C, self.psi2_scaled, self.Kmmi) + self.Kmmi) # dC
+        self.dL_dKmm +=  np.dot(np.dot(self.E*sf2, self.beta*self.psi2_scaled) - np.dot(self.C, self.psi1VVpsi1), self.Kmmi) + 0.5*self.E # dD
+
+    def log_likelihood(self):
+        """ Compute the (lower bound on the) log marginal likelihood """
+        sf2 = self.scale_factor**2
+        A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta)) -0.5*self.beta*self.trYYT
+        B = -0.5*self.D*(self.beta*self.psi0-np.trace(self.A)*sf2)
+        C = -0.5*self.D * (self.B_logdet + self.M*np.log(sf2))
+        D = +0.5*np.sum(self.psi1VVpsi1 * self.C)
+        return A+B+C+D
+
+    def set_param(self, p):
+        self.Z = p[:self.M*self.Q].reshape(self.M, self.Q)
+        self.beta = p[self.M*self.Q]
+        self.kern.set_param(p[self.Z.size + 1:])
+        self.beta2 = self.beta**2
+        self._compute_kernel_matrices()
+        self._computations()
 
     def get_param(self):
         return np.hstack([self.Z.flatten(),self.beta,self.kern.extract_param()])
@@ -113,30 +132,19 @@ class sparse_GP_regression(GP_regression):
     def get_param_names(self):
         return sum([['iip_%i_%i'%(i,j) for i in range(self.Z.shape[0])] for j in range(self.Z.shape[1])],[]) + ['noise_precision']+self.kern.extract_param_names()
 
-    def log_likelihood(self):
-        """
-        Compute the (lower bound on the) log marginal likelihood
-        """
-        A = -0.5*self.N*self.D*(np.log(2.*np.pi) - np.log(self.beta))
-        B = -0.5*self.beta*self.D*self.trace_K
-        C = -0.5*self.D * self.B_logdet
-        D = -0.5*self.beta*self.trYYT
-        E = +0.5*np.sum(self.psi1VVpsi1 * self.LBL_inv)
-        return A+B+C+D+E
-
     def dL_dbeta(self):
         """
         Compute the gradient of the log likelihood wrt beta.
         """
         #TODO: suport heteroscedatic noise
-        dA_dbeta =   0.5 * self.N*self.D/self.beta
-        dB_dbeta = - 0.5 * self.D * self.trace_K
+        sf2 = self.scale_factor**2
+        dA_dbeta =   0.5 * self.N*self.D/self.beta - 0.5 * self.trYYT
+        dB_dbeta = - 0.5 * self.D * self.psi0 - np.trace(self.A)/self.beta*sf2
         dC_dbeta = - 0.5 * self.D * np.sum(self.Bi*self.A)/self.beta
-        dD_dbeta = - 0.5 * self.trYYT
-        tmp = mdot(self.LBi.T, self.LLambdai, self.psi1V)
-        dE_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
+        tmp = mdot(self.Bi, self.Lmi, self.psi1V)
+        dD_dbeta = (np.sum(np.square(self.C)) - 0.5 * np.sum(self.A * np.dot(tmp, tmp.T)))/self.beta
 
-        return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta + dE_dbeta)
+        return np.squeeze(dA_dbeta + dB_dbeta + dC_dbeta + dD_dbeta)
 
     def dL_dtheta(self):
         """