A finite-difference method for heat conduction with phase change proposed by Hsiao [7] is shown to be equivalent to that of Comini et al. [9]. The method is extended to cover the case of gradual phase change and compared to several others. A small but consistent error is found in the method. The fastest method is a Crank-Nicolson version of Pham's method [5]. The explicit enthalpy method, though slower, is suitable for casual users.