diff --git a/GPy/likelihoods/Gaussian.py b/GPy/likelihoods/Gaussian.py
index e08fee90..d87b1b98 100644
--- a/GPy/likelihoods/Gaussian.py
+++ b/GPy/likelihoods/Gaussian.py
@@ -51,11 +51,15 @@ class Gaussian(likelihood):
         return ["noise_variance"]
 
     def _set_params(self, x):
-        x = float(x)
+        x = np.float64(x)
         if self._variance != x:
-            self.precision = 1. / x
+            if x == 0.:
+                self.precision = None
+                self.V = None
+            else:
+                self.precision = 1. / x
+                self.V = (self.precision) * self.Y
             self.covariance_matrix = np.eye(self.N) * x
-            self.V = (self.precision) * self.Y
             self._variance = x
 
     def predictive_values(self, mu, var, full_cov):