Recent estimates of Antarctica's present-day rate of ice-mass contribution to changes in sea level range from 31 gigatonnes a year (Gt yr-1 ref. 1) to 246 Gt yr-1 (ref. 2), a range that cannot be reconciled within formal errors. Time-varying rates of mass loss contribute to this, but substantial technique-specific systematic errors also exist. In particular, estimates of secular ice-mass change derived from Gravity Recovery and Climate Experiment (GRACE) satellite data are dominated by significant uncertainty in the accuracy of models of mass change due to glacial isostatic adjustment (GIA). Here we adopt a new model of GIA, developed from geological constraints, which produces GIA rates systematically lower than those of previous models, and an improved fit to independent uplift data. After applying the model to 99 months (from August 2002 to December 2010) of GRACE data, we estimate a continent-wide ice-mass change of -69 +/- 18 Gt yr-1 (+0.19 +/- 0.05 mm yr-1 sea-level equivalent). This is about a third to a half of the most recently published GRACE estimates, which cover a similar time period but are based on older GIA models. Plausible GIA model uncertainties, and errors relating to removing longitudinal GRACE artefacts (`destriping'), confine our estimate to the range -126 Gt yr-1 to -29 Gt yr-1 (0.08-0.35 mm yr-1 sea-level equivalent). We resolve 26 independent drainage basins and find that Antarctic mass loss, and its acceleration, is concentrated in basins along the Amundsen Sea coast. Outside this region, we find that West Antarctica is nearly in balance and that East Antarctica is gaining substantial mass.