In this paper we generalize the results of an earlier paper to describe a moving breather in a discrete sine - Gordon system. The method uses the calculus of variations and perturbation theory to find the discreteness effects of a breather moving through a nonlinear Klein - Gordon lattice. These results are then used to calculate the energy contained in a discrete breather and this is shown to be less than the corresponding breather in a continuous system. The second part of the paper considers the variation of kinetic and potential energies with position of breather; these variations are analysed using Peierls - Nabarro-type calculations. The results of this analysis show that small amplitude breathers can move through a lattice almost unhindered by discreteness, thus demonstrating recent results of MacKay and Aubry.