In recent years, great improvements have been made toward understanding the modern dynamics and recent history of the ice sheets. Several recently-launched satellite missions promise to make geodesy the most powerful tool for investigation of the changing ice sheets, including their past history and their present behavior. Mathematical description of ice sheet behavior from geodetic data requires accurate modeling of all the processes which may affect the measurements. Most geodetic tools measure changes in elevation of the ice sheets, which can include Post Glacial Rebound (PGR), the current Ice Mass Trend (IMT) consisting of both accumulation and glacial outflux, and processes of compaction within the firn column. Consequently it is necessary for mathematical models of geodetic data to separate the effects of IMT, PGR, and compaction. Satellite measurements of the time-variable geoid are insensitive to compaction effects and depend on IMT and PGR differently than do height measurements. Two methodological approaches have been proposed to separate these effects using measurements of height and time-variable geoid: 1- direct inversion for ice mass variability (Wu et al., 2002), which requires a priori assumptions about either the Earth’s rheology or the ice load history; 2- iterative solution for the fields, which theoretically is more approximate but is computationally much simpler and less dependent on a priori assumptions. In this paper we analyze how we can learn about IMT and PGR by combining geodetic measurements, and we assess the conditions required to optimally combine satellite and ground-based data sets.