Ice loss from the Greenland and Antarctic ice sheets currently contributes one third of global sea level rise, yet monitoring their complex coastal regions remains a challenge. One of the principal methods for determining ice sheet imbalance is satellite radar altimetry, which provides a 30-year record of surface elevation change. Over rugged coastal topography, however, the altimeter echo returned from the ice sheet surface is often complex, with multiple distinct surface reflections degrading the accuracy of elevation measurements. Here, we present a new processing approach, termed the MultiPeak Ice (MPI) reprocessing strategy. This method is designed specifically for complex ice surfaces, where the majority of ice mass imbalance occurs, and is able to reliably retrieve multiple elevation measurements from a single altimetry echo. We apply this new approach to Sentinel-3 non-interferometric delay-Doppler altimeter echoes acquired over the Greenland Ice Sheet and demonstrate its capability to improve both the accuracy and the quantity of elevation measurements. Through comparison with coincident airborne and satellite laser altimetry we show that our MPI processing increases the number of elevation measurements by 31%, reduces the mean biases observed in conventional Level-2 processing from 4.3 m to 0.6 m, and lowers the outlier percentage (from 15% to 2%). Our new approach has the potential to extend the operational capability of non-interferometric radar altimeters over complex glaciological targets and ultimately to improve estimates of ice sheet mass imbalance.