diff --git a/GPy/kern/parts/prod.py b/GPy/kern/parts/prod.py
index e386a292..7441ae9f 100644
--- a/GPy/kern/parts/prod.py
+++ b/GPy/kern/parts/prod.py
@@ -19,7 +19,10 @@ class Prod(Kernpart):
     """
     def __init__(self,k1,k2,tensor=False):
         self.num_params = k1.num_params + k2.num_params
-        self.name = '['+k1.name + '**' + k2.name +']'
+        if tensor:
+            self.name = '['+k1.name + '**' + k2.name +']'
+        else:
+            self.name = '['+k1.name + '*' + k2.name +']'
         self.k1 = k1
         self.k2 = k2
         if tensor:
@@ -130,13 +133,12 @@ class Prod(Kernpart):
                 self.k1.K(X[:,self.slice1],X2[:,self.slice1],self._K1)
                 self.k2.K(X[:,self.slice2],X2[:,self.slice2],self._K2)
 
-    def getstate(self):
-        return [self._get_params(), self.k1, self.k2, self.slice1, self.slice2, self.name]
+    def __getstate__(self):
+        return [self.k1, self.k2, self.slice1, self.slice2, self.name, self.input_dim, self.num_params]
 
-    def setstate(self, state):
-        params, self.k1, self.k2, self.slice1, self.slice2, self.name = state
+    def __setstate__(self, state):
+        self.k1, self.k2, self.slice1, self.slice2, self.name, self.input_dim, self.num_params = state
         self._X, self._X2, self._params = np.empty(shape=(3,1))
-        self._set_params(params)