The essential feature of the Kawasaki model is the conserved order parameter, which places the model in class B of the Halperin, Hoheberg, and Ma classification. We have studied the energy relaxation of this model in one and two dimensions with the added feature that spin exchange may take place between any pair of sites within the system. Our results for the dynamic exponent z are indistinguishable from those for class A models, in which the order parameter is not conserved.