Global sea level is an indicator of climate change(1-3), as it is sensitive to both thermal expansion of the oceans and a reduction of land-based glaciers. Global sea-level rise has been estimated by correcting observations from tide gauges for glacial isostatic adjustment-the continuing sea-level response due to melting of Late Pleistocene ice-and by computing the global mean of these residual trends(4-9). In such analyses, spatial patterns of sealevel rise are assumed to be signals that will average out over geographically distributed tide-gauge data. But a long history of modelling studies(10-12) has demonstrated that non-uniform- that is, non-eustatic-sea-level redistributions can be produced by variations in the volume of the polar ice sheets. Here we present numerical predictions of gravitationally consistent patterns of sea-level change following variations in either the Antarctic or Greenland ice sheets or the melting of a suite of small mountain glaciers. These predictions are characterized by geometrically distinct patterns that reconcile spatial variations in previously published sea-level records. Under the-albeit coarse-assumption of a globally uniform thermal expansion of the oceans, our approach suggests melting of the Greenland ice complex over the last century equivalent to similar to0.6 mm yr(-1) of sea-level rise.