diff --git a/GPy/likelihoods/Laplace.py b/GPy/likelihoods/Laplace.py
index b1b41957..b5c0bdfe 100644
--- a/GPy/likelihoods/Laplace.py
+++ b/GPy/likelihoods/Laplace.py
@@ -1,11 +1,12 @@
 import numpy as np
 import scipy as sp
 import GPy
-from scipy.linalg import cholesky, eig, inv, cho_solve, det
+from scipy.linalg import inv, cho_solve, det
 from numpy.linalg import cond
 from GPy.likelihoods.likelihood import likelihood
 from GPy.util.linalg import pdinv, mdot, jitchol, chol_inv, det_ln_diag, pddet
 from scipy.linalg.lapack import dtrtrs
+import pylab as plt
 
 
 class Laplace(likelihood):
@@ -62,7 +63,7 @@ class Laplace(likelihood):
         return self.likelihood_function._get_param_names()
 
     def _set_params(self, p):
-        return self.likelihood_function._set_params()
+        return self.likelihood_function._set_params(p)
 
     def both_gradients(self, dL_d_K_Sigma, dK_dthetaK):
         """
@@ -77,8 +78,8 @@ class Laplace(likelihood):
         return (self._Kgradients(dL_d_K_Sigma, dK_dthetaK), self._gradients(dL_d_K_Sigma))
 
     def _shared_gradients_components(self):
-        dL_dytil = -np.dot((self.K+self.Sigma_tilde), self.Y)
-        dytil_dfhat = np.dot(self.Sigma_tilde, self.Ki) + np.eye(self.N) # or self.Wi__Ki_W?
+        dL_dytil = -np.dot(self.Y.T, (self.K+self.Sigma_tilde))
+        dytil_dfhat = self.Wi__Ki_W # np.dot(self.Sigma_tilde, self.Ki) + np.eye(self.N) # or self.Wi__Ki_W?
         return dL_dytil, dytil_dfhat
 
     def _Kgradients(self, dL_d_K_Sigma, dK_dthetaK):
@@ -91,12 +92,18 @@ class Laplace(likelihood):
         """
         dL_dytil, dytil_dfhat = self._shared_gradients_components()
 
-        I_KW_i, _, _, _ = pdinv(np.eye(self.N) + np.dot(self.K, self.W))
+        A = np.eye(self.N) + np.dot(self.K, self.W)
+        plt.imshow(A)
+        plt.show()
+        I_KW_i, _, _, _ = pdinv(A)
+
         #FIXME: Careful dK_dthetaK is not the derivative with respect to the marginal just prior K!
-        dfhat_dthetaK = I_KW_i*dK_dthetaK*self.likelihood_function.link_grad(self.data, self.f_hat, self.extra_data)
-
-        dytil_dthetaK = dytil_dfhat*dfhat_dthetaK
+        #Derivative for each f dimension, for each of K's hyper parameters
+        dfhat_dthetaK = np.zeros((self.f_hat.shape[0], dK_dthetaK.shape[0]))
+        for ind_j, thetaj in enumerate(dK_dthetaK):
+            dfhat_dthetaK[:, ind_j] = mdot(I_KW_i, thetaj, self.likelihood_function.link_grad(self.data, self.f_hat, self.extra_data))
 
+        dytil_dthetaK = np.dot(dytil_dfhat, dfhat_dthetaK) # should be (D,thetaK)
         #FIXME: Careful dL_dK = dL_d_K_Sigma
         #FIXME: Careful the -D*0.5 in dL_d_K_sigma might need to be -0.5?
         dL_dSigma = dL_d_K_Sigma
@@ -105,8 +112,9 @@ class Laplace(likelihood):
         dSigmai_dthetaK = 0 #+ np.sum(d3phi_d3fhat*dfhat_dthetaK) #FIXME: CAREFUL OF THIS SUM! SHOULD SUM OVER FHAT NOT THETAS
         dSigma_dthetaK = -mdot(self.Sigma_tilde, dSigmai_dthetaK, self.Sigma_tilde)
 
-        dL_dthetaK_implicit = dL_dytil*dytil_dthetaK + dL_dSigma*dSigma_dthetaK
-        return dL_dthetaK_implicit
+        dL_dthetaK_implicit = np.sum(np.dot(dL_dytil, dytil_dthetaK), axis=0)# + np.dot(dL_dSigma, dSigma_dthetaK)
+        #dL_dthetaK_implicit = np.dot(dL_dytil.T, dytil_dthetaK.T)
+        return np.squeeze(dL_dthetaK_implicit)
 
     def _gradients(self, partial):
         """
@@ -132,16 +140,25 @@ class Laplace(likelihood):
         partial = dL_dK
         """
         dL_dytil, dytil_dfhat = self._shared_gradients_components()
-        dfhat_dthetaL = self.likelihood_function.df_dtheta()
+        dfhat_dthetaL, dSigmai_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat, self.extra_data) #FIXME: Shouldn't this have a implicit component aswell?
 
-        dSigmai_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat, self.extra_data) #FIXME: Shouldn't this have a implicit component aswell?
-        dSigma_dthetaL = -mdot(self.Sigma_tilde, dSigmai_dthetaL, self.Sigma_tilde)
+        #dSigmai_dthetaL = self.likelihood_function._gradients(self.data, self.f_hat, self.extra_data) #FIXME: Shouldn't this have a implicit component aswell?
+        #Derivative for each f dimension, for each of K's hyper parameters
+        dSigma_dthetaL = np.empty((self.N, len(self.likelihood_function._get_param_names())))
+        for ind_l, dSigmai_dtheta_l in enumerate(dSigmai_dthetaL.T):
+            dSigma_dthetaL[:, ind_l] = -mdot(self.Sigma_tilde,
+                                             dSigmai_dtheta_l, # Careful, shouldn't this be (N, 1)?
+                                             self.Sigma_tilde
+                                             )
+
+        #TODO: This is Wi*A*Wi, can be more numerically stable with a trick
+        #dSigma_dthetaL = -mdot(self.Sigma_tilde, dSigmai_dthetaL, self.Sigma_tilde)
         dL_dSigma = partial # partial is dL_dK but K here is K+Sigma_tilde.... which is fine in this case
 
-        dytil_dthetaL = dytil_dfhat*dfhat_dthetaL
-        dL_dthetaL = 0 + dL_dytil*dytil_dthetaL + dL_dSigma*dSigma_dthetaL
-        return dL_dthetaL
-        #return np.zeros(0)  # TODO: Laplace likelihood might want to take some parameters...
+        #dytil_dthetaL = dytil_dfhat*dfhat_dthetaL
+        dytil_dthetaL = np.dot(dytil_dfhat, dfhat_dthetaL)
+        dL_dthetaL = 0 + np.dot(dL_dytil, dytil_dthetaL)# + np.dot(dL_dSigma, dSigma_dthetaL)
+        return np.squeeze(dL_dthetaL) #should be array of length *params-being optimized*, for student t just optimising 1 parameter, this is (1,)
 
     def _compute_GP_variables(self):
         """
@@ -335,7 +352,7 @@ class Laplace(likelihood):
         rs = 0
         i = 0
         while difference > epsilon and i < MAX_ITER and rs < MAX_RESTART:
-            f_old = f.copy()
+            #f_old = f.copy()
             W = -np.diag(self.likelihood_function.link_hess(self.data, f, extra_data=self.extra_data))
             if not self.likelihood_function.log_concave:
                 W[W < 0] = 1e-6     # FIXME-HACK: This is a hack since GPy can't handle negative variances which can occur
diff --git a/GPy/likelihoods/likelihood_functions.py b/GPy/likelihoods/likelihood_functions.py
index 6e72b029..64791047 100644
--- a/GPy/likelihoods/likelihood_functions.py
+++ b/GPy/likelihoods/likelihood_functions.py
@@ -159,10 +159,10 @@ class student_t(likelihood_function):
     d2ln p(yi|fi)_d2fifj
     """
     def __init__(self, deg_free, sigma=2):
-        super(student_t, self).__init__()
         self.v = deg_free
         self.sigma = sigma
         self.log_concave = False
+        #super(student_t, self).__init__()
 
     def _get_params(self):
         return np.asarray(self.sigma)
@@ -258,9 +258,9 @@ class student_t(likelihood_function):
                      )
         return d3link_d3f
 
-    def link_hess_grad_sigma(self, y, f, extra_data=None):
+    def link_hess_grad_std(self, y, f, extra_data=None):
         """
-        Gradient of the hessian w.r.t sigma parameter
+        Gradient of the hessian w.r.t sigma parameter (standard deviation)
 
         $$\frac{2\sigma v(v+1)(\sigma^{2}v - 3(f-y)^2)}{((f-y)^{2} + \sigma^{2}v)^{3}}
         """
@@ -273,8 +273,24 @@ class student_t(likelihood_function):
                           )
         return hess_grad_sigma
 
+    def link_grad_std(self, y, f, extra_data=None):
+        """
+        Gradient of the likelihood w.r.t sigma parameter (standard deviation)
+
+        $$\frac{-2\sigma(v+1)(y-f)}{(v\sigma^{2} + (y-f)^{2})^{2}}$$
+        """
+        y = np.squeeze(y)
+        f = np.squeeze(f)
+        assert y.shape == f.shape
+        e = y - f
+        grad_sigma = (  (-2*self.sigma*self.v*(self.v + 1)*e)
+                      / ((self.v*(self.sigma**2) + e**2)**2)
+                     )
+        return grad_sigma
+
     def _gradients(self, y, f, extra_data=None):
-        return [self.link_hess_grad_sigma] # list as we might learn many parameters
+        return [self.link_grad_std(y, f, extra_data=extra_data)[:, None],
+                self.link_hess_grad_std(y, f, extra_data=extra_data)[:, None]] # list as we might learn many parameters
 
     def predictive_values(self, mu, var):
         """
@@ -372,9 +388,7 @@ class weibull_survival(likelihood_function):
     def __init__(self, shape, scale):
         self.shape = shape
         self.scale = scale
-
-        #FIXME: This should be in the superclass
-        self.log_concave = True
+        self.log_concave = True # Or false?
 
     def link_function(self, y, f, extra_data=None):
         """
diff --git a/GPy/models/GP.py b/GPy/models/GP.py
index 1024b5ef..24037afe 100644
--- a/GPy/models/GP.py
+++ b/GPy/models/GP.py
@@ -128,17 +128,17 @@ class GP(model):
 
         For the likelihood parameters, pass in alpha = K^-1 y
         """
+        dL_dthetaK = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
         if isinstance(self.likelihood, Laplace):
-            dL_dthetaK_explicit = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
+            dL_dthetaK_explicit = dL_dthetaK
             #Need to pass in a matrix of ones to get access to raw dK_dthetaK values without being chained
             fake_dL_dKs = np.ones(self.dL_dK.shape)
             dK_dthetaK = self.kern.dK_dtheta(dL_dK=fake_dL_dKs, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
 
             dL_dthetaK_implicit = self.likelihood._Kgradients(self.dL_dK, dK_dthetaK)
             dL_dthetaK = dL_dthetaK_explicit + dL_dthetaK_implicit
-            dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
+            dL_dthetaL = self.likelihood._gradients(partial=self.dL_dK)
         else:
-            dL_dthetaK = self.kern.dK_dtheta(dL_dK=self.dL_dK, X=self.X, slices1=self.Xslices, slices2=self.Xslices)
             dL_dthetaL = self.likelihood._gradients(partial=np.diag(self.dL_dK))
         return np.hstack((dL_dthetaK, dL_dthetaL))
 
diff --git a/GPy/util/linalg.py b/GPy/util/linalg.py
index cb899397..20293ed8 100644
--- a/GPy/util/linalg.py
+++ b/GPy/util/linalg.py
@@ -25,7 +25,7 @@ def pddet(A):
     """
     Determinant of a positive definite matrix
     """
-    L = cholesky(A)
+    L = jitchol(A)
     logdetA = 2*sum(np.log(np.diag(L)))
     return logdetA