The single-crystal neutron diffuse scattering from ice contains a great deal of information, not only on the disorder of the hydrogen atoms but also on the instantaneous atomic positions. It is difficult to extract this information, and a series of reverse Monte Carlo (RMC) techniques have been developed for this purpose, with mixed success. The present paper presents new constrained RMC methods used to try and obtain more reliable information on the static and thermal disorder in ice. However it has been found that the RMC results depend strongly on the starting configuration, meaning that some of the conclusions of the earlier paper of Nield and Whitworth (Nield, V. M.; Whitworth, R. W. J. Phys. : Condens. Matter 1995, 7, 8258) are invalid.