Four scenarios of present day Antarctic ice sheet mass change are developed from comprehensive reviews of the available glaciological and oceanographic evidence. The gridded scenarios predict widely varying contributions to secular sea level change &xgr;˙ ranging from -1.1 to 0.45 mm/yr, and predict polar motion m˙ and time-varying low-degree gravitational coefficients J˙l that differ significantly from earlier estimates. A reasonably linear relationship between the rate of sea level change from Antarctica &xgr;˙A and the predicted Antarctic J˙l is found for the four scenarios. This linearity permits a series of forward models to be constructed that incorporate the effects of ice mass changes in Antarctica, Greenland, and distributed smaller glaciers, as well as postglacial rebound (assuming the ICE-3G deglaciation history), with the goal of obtaining optimum reconciliation between observed constraints on J˙l and sea level rise &xgr;˙. Numerous viable combinations of lower mantle viscosity and hydrologic sources are found that satisfy observed &xgr;˙ in the range of 1 to 2--2.5 mm/yr and observed J˙l for degrees 2, 3, and 4. In contrast, rates of global sea level rise above 2.5 mm/yr are inconsistent with available J˙l observations. The successful composite models feature a pair of lower mantle viscosity solutions arising from the sensitivity of J˙l to glacial rebound. The paired values are well separated at &xgr;˙=1 mm/yr, but move closer together as &xgr;˙ is increased, and, in fact, merge around &xgr;˙=2--2.5 mm/yr, revealing an intimate relation between &xgr;˙ and preferred lower mantle viscosity. This general pattern is quite robust and persists for different J˙l solutions, for variations in source assumptions, and for different styles of lower mantle viscosity stratification. Tighter J˙l constraints for l>2 may allow some viscosity stratification schemes and source assumptions to be excluded in the future. For a given total observed &xgr;˙, the sea level rise from Antarctica &xgr;˙A is tightly constrained and ranges from 0 to +1 mm/yr (corresponding to an ablating ice sheet) as estimates of &xgr;˙ are raised from 1 to 2.5 mm/yr. However, when the degree 3 zonal harmonic constraint is removed, the solutions show little sensitivity to Antarctic mass balance, emphasizing the need for a well determined odd-degree secular zonal harmonic for determining polar ice mass balance.¿ 1997 American Geophysical Union