This study uses a finite element numerical method to analyze the effect of a low-viscosity zone on convection driven by heating from below in the upper mantle. A swell results from the surface expression of the convection cell. The viscosity structure of the upper mantle has been approximated by three layers consisting of a conducting lid which overlies a low-viscosity layer which in turn overlies a constant viscosity layer extending to the base of the upper mantle. The low-viscosity zone causes the top boundary layer of the convection cell to thin, and at high viscosity contrasts and Rayleigh numbers, it can cause the boundary layer to go unstable. The low-viscosity zone also alters the response of the surface observables to the temperature anomalies. In particular, it mitigates the transmission of normal stress to the conducting lid so that the topography and geoid anomalies decrease. The geoid anomaly decreases faster than the topography anomaly, however, so that the depth of compensation can appear to be well within the conducting lid. Because the boundary layer is thinned, the elastic plate thickness also decreases, and since the low viscosity allows the fluid to flow faster in the top layer, the uplift time decreases as well. We have compared the results of this modeling to data at the Hawaii, Bermuda, Cape Verde, and Marquesas swells and have found that it can reproduce their observed anomalies. The viscosity contrasts that are required range from 0.2 to 0.01 and decrease as the age of the swell increases. These magnitudes and the trend with age are consistent with theoretical and other estimates of the viscosity variation in the shallow upper mantle. Convective models can therefore explain the uplift and observed anomalies at midplate swells. ¿ American Geophysical Union 1988