The deepest geoid low globally with respect to hydrostatic equilibrium is in the Ross Sea area. Nearby in West Antarctica is a residual topography high. Both are in a region with thin lithosphere, where a mantle plume has been suggested. Hence upper mantle viscosity could be regionally reduced, allowing for faster rebound than elsewhere upon melting of the West Antarctic Ice Sheet, one of the global climate system’s tipping elements. To study possible causes of the geoid low / topography high combination, we compute the effects of disk-shaped density anomalies. With -1% density anomaly and a global average radial viscosity structure, geoid low and topography high can be explained with disk radius about 10° and depth range ~150-650 km. Alternatively, there may be two separate disks somewhat laterally displaced, one just below the lithosphere and mainly causing a dynamic topography high and one below the transition zone causing the geoid low. If viscosity in the uppermost mantle is reduced by a factor 10 (from 50 to 350 km depth) to 100 (from 100 to 220 km), one shallow disk in the depth range 50-350 km would also be sufficient. In order to test the feasibility of such density models, we perform computations of a thermal plume that enters at the base of a cartesian box corresponding to a region in the upper mantle, as well as some whole-mantle thermal plume models, with ASPECT. These plume models have typically a narrow conduit and the plume tends to only become wider as it spreads beneath the lithosphere, typically shallower than ~300 km. These results are most consistent with the shallow disk model with reduced uppermost mantle viscosity, hence providing further support for such low viscosities beneath West Antarctica.