A new high resolution global model of late Pleistocene deglaciation is inferred on the basis of geophysical predictions of postglacial relative sea level variations in which the ice-ocean-solid Earth interaction is treated in a gravitationally self-consistent fashion. For the purpose of these analyses the radial viscoelastic structure of the planet is assumed known on the basis of previously published sensitivity tests on solutions of the forward problem. Only radiocarbon controlled relative sea level histories from sites that were actually ice covered (with one or two additions) are employed to constrain the model, leaving relative sea level (RSL) data from sites that were not ice covered to be employed to confirm its consistency. Results for these confirmatory analyses are reported elsewhere. Here the new deglaciation model, referred to as ICE-3G, is compared to previous models derived by several independent means and tested against a number of additional observations other than sea level histories, including geologically controlled retreat isochrones, oxygen-isotope data from deep-sea sedimentary cores, and coral terrace elevations. The latter two observations strongly constrain the net sea level rise that has occurred since the onset of deglaciation and therefore the mass of ice that melted during the last glacial-interglacial transition.