In this work, it is shown that the similarities between discretized and continuum models of water are heavily dependent upon the exact value of the discretization parameter, zeta, defined as the ratio of the Lennard-Jones size parameter sigma to the lattice spacing. For example, some discretized models layered into a hexagonal ice-like structure at temperatures up to 550 K. A discretization parameter of zeta = 13 was chosen such that the radial distribution function of the liquid at 298 K for the lattice model closely matched the continuum. This discretized model is capable of reproducing the low-temperature phase diagram with the advantage of significant CPU time savings. (C) 2004 Elsevier B.V. All rights reserved.