Models of glacio-hydro-isostatic rebound and the concomitant sea-level change have been progressively improved over the past three decades. Recently, the procedures used by the group at the Australian National University (ANU) for the hydro-isostatic component of the theory have been questioned (Quat. Sci. Rev. 21 (2002) 409) although the details of the ANU group's procedures have not been published because they are mainly computational in nature rather than representing significant conceptual advances. Because of this criticism, we set out here in detail the procedures that have been used for the treatment of the migration of shorelines as sea levels rise and fall, the effect of retreat and advancing grounded ice on shelves and shallow seas, and the transitions from grounded to floating ice (and vice versa). We conclude that there is no basis for the criticism, that these formulations and their implementation provide a high resolution and complete description of both sea-level change and of the estimates of volumes of ice exchanged with the oceans. The results from this formulation are confirmed by the entirely independent analyses of Milne et al. (Quat. Sci. Rev. 21 (2002) 361) and Mitrovica and Milne (Geophys. J. Int. (2002), submitted for publication) who conclude that our formulation is significantly more accurate than the procedure advocated by Peltier (Science 265 (1994) 195; Rev. Geophys. 36 (1998a) 603, Geophys. Res. Lett. 25 (1998b) 3955). (C) 2002 Published by Elsevier Science Ltd.