One of the most powerful constraints on mantle viscosity comes from the correlation of the long-wavelength (degree 4--9) geoid with that predicted by a density model for subducted slabs. The effect of lateral variations of viscosity should be most pronounced at subduction zones, due to the strong effect of temperature on viscosity. An idealized slab model with temperature-dependent viscosity is considered, with various lateral and vertical viscosity structures, using a two-dimensional finite element formulation. The viscosity parameterization affects the amplitude of the long-wavelength geoid anomaly but not the sign of the correlation between the geoid and density anomalies. Depth-dependent viscosity models with a high-viscosity lithospheric layer do not completely match the temperature-dependent (laterally varying) results, suggesting that the rheology of the slab does have an effect on the long-wavelength surface topography and geoid; however, this affect is minor, suggesting that the radial models of mantle viscosity inferred from surface observables are correct to first order. In contrast, the short-wavelength features are dramatically affected by the rheology of the region surrounding the downwelling. Further study of the shorter-wavelength geoid over subduction zones may provide better insight into subduction zone processes. ¿ American Geophysical Union 1994