Projections of future global sea level critically depend on reliable estimates of mass balance changes on the polar ice sheets. The most sophisticated tools allowing for such estimates are General Circulation Models (GCM). A major impediment until recently has been their coarse grid resolution (3°–6°) causing substantial uncertainties in the mass balance calculations on the poorly resolved ice sheets. The present study is based on a climate change experiment of highest resolution currently feasible (T106, 1.1°). The precipitation distribution significantly benefits from the more realistic orographic forcing in the high-resolution experiment and is very accurately reproduced. A greenhouse warming experiment with doubled carbon-dioxide concentration based on the same high-resolution model suggests an increase in accumulation on both Greenland and Antarctic ice sheets. On the other hand, even a T106 resolution is still too coarse for the simulation of ablation on the narrow ice sheet margins, where most of the melting takes place. A simple method is presented to improve ablation diagnostics from GCMs, based on the interpolation of the reference temperature and temperature anomaly fields onto a fine mesh topography of 2 km horizontal resolution. The increase in ablation on Greenland in the greenhouse scenario is thereby smaller than the increase directly inferred from the GCM grid. As for Antarctica, it is still too cold at the time of doubled carbon-dioxide concentration for significant ablation. The results from the greenhouse experiment with doubled carbon-dioxide concentration thus suggest not only a mass gain in Antarctica due to the increase in accumulation, but also a mass gain in Greenland, since the enhanced ablation in the warmer climate does not fully compensate for the increased accumulation. In terms of global sea level change, these mass balance shifts correspond to a net sea level decrease of 1.2 mm y−1 at the time of doubled carbon-dioxide. This may compensate for a substantial fraction of the melt-induced sea level rise from smaller glaciers and ice caps, leaving thermal expansion as the dominant factor for sea level rise over the coming decades. The compensating effect, however, could fade if carbon-dioxide concentrations in the atmosphere cannot be stabilized and continue to rise above double the present values, since the associated greenhouse warming could then become large enough to induce significant melting also on the Antarctic ice sheet.