We compare rates of surface-elevation change on the Greenland ice sheet derived from European Remote-sensing Satellite-2 (ERS-2) radar-altimeter data with those obtained from laser-altimeter data collected over nearly the same time periods. Radar-altimeter data show more rapid thickening (9 ± 1 cm a−1 above 1500 m elevation in the north, and 3 ± 1 cm a−1 above 2000 m in the south) than the laser estimates, possibly caused by a lifting of the radar-reflection horizon associated with changes in the snowpack, such as those caused by progressively increased surface melting, as summer temperatures rise. Over all the ice sheet above 2000 m, this results in an ERS-derived volume balance ∼75 ± 15 km3 a−1 more positive than that from laser data. This bias between laser and radar estimates of elevation change varies spatially and temporally, so cannot at present be corrected without independent surveys such as those presented here. At lower elevations, comparison of detailed repeat laser surveys over Jakobshavn Isbræ with ERS results over the same time interval shows substantial ERS underestimation of ice-thinning rates. This results partly from missing data because of ‘bad’ radar waveforms over the very rough surface topography, and partly from the tendency for large radar footprints to sample preferentially local high points in the topography, thus missing regions of most rapid thinning along glacier depressions.