Airborne radar sounding is difficult in South Greenland because of the presence of englacial water, which prevents the signal from reaching the bed. Data coverage remains suboptimal for traditional methods of ice-thickness and bed mapping that rely on geostatistical techniques, such as kriging, because important features are missing. Here we apply two alternative approaches of highresolution (̃300 m) ice-thickness mapping, that are based on the conservation of mass, to two regions of South Greenland: (1) Qooqqup Sermia and Kiattuut Sermiat, and (2) Ikertivaq. These two algorithms solve optimization problems, for which the conservation of mass is either enforced as a hard constraint, or as a soft constraint. For the first region, very few measurements are available but there is no gap in ice motion data, whereas for Ikertivaq, more ice-thickness measurements are available, but there are gaps in ice motion data. We show that mass-conservation algorithms can be used as validation tools for radar sounding. We also show that it is preferable to apply mass conservation as a hard constraint, rather than a soft constraint, as it better preserves elongated features, such as glacial valleys and ridges.