We investigate the accuracy and resolution of estimating global ice mass variations using secular gravity and ice elevation change observations by the planned Gravity Recovery and Climate Experiment (GRACE) and ICESat missions. The gravity and altimetry data combination can determine the total bedrock uplift rate with root-mean-square (RMS) errors of 0.2--1.3 mm/yr when Gaussian averaged over a half scale of 250 km. Moreover, covariance analyses indicate that the mean snow compaction error can be constrained to the level of 3 mm/yr in equivalent Antarctic ice thickness change. The mean Antarctic present-day ice mass change could then be determined to about 4 mm/yr. For a known viscosity profile, such data sets provide a spatial estimate of a linear combination of the late Pleistocene deglaciation and a more recent past trend (last few thousand years) in the Greenland and Antarctica mass balance. For example, when the linear rate of the recent past trend is estimated solely for ice history, the RMS errors of the 450-km Gaussian averages range between 1 and 3 cm/yr. Although contaminated by the signature of present-day hydrological variations over the deglaciated areas, the 450-km Gaussian-averaged Last Glacial Maximum height of the ancient ice sheets can be determined to a RMS level of 300 m. The mean recovery errors are less than 100 m. However, the gravity/altimeter data cannot resolve the load history and lower mantle viscosity simultaneously. Additional data such as relative sea level records must be invoked to overcome this difficulty.