Using a previously developed non-pair-additive model of the water–water hydrogen bond, the relative stabilites of hydrogen ordered and disordered ice Ih, ices VII and VIII are examined. The results are consistent with both the observed hydrogen-ordering in the VII → VIII transition, and the lack of any similar ordering in hexagonal ice I. The symmetry relation between the two sub-lattices of VII and VIII, together with the non-linearity of the energy of the dipole–dipole interaction, suggest such ordering transitions may be favoured only when very special symmetry arrangements result in the cancellation of certain electropole energy terms.