Spectral analysis of a recently obtained high resolution tomographic model, describing the top 1200 km of the mantle, shows a power-law dependence on the degree, for degrees greater than around 10. The spectrum of recent geoid models is also found to decay in a linear fashion with degree on a log-log plot. We have employed the logarithmic slope of the geoid between degrees 10 and 25 as a constraint on the viscosity structure of the top 1200 km of the mantle. The constraint of fitting the geoid slope represents a new and independent approach to the determination of the upper-mantle viscosity structure. From conducting over one million runs in a Monte Carlo inversion, we have found that there are basically three families of viscosity which can fit the geoid slope. They are (1) with a viscosity hill between 660 and 1000 km, (2) with a weak viscosity increase at 660 km, and (3) with a significant viscosity increase at depths between 820 and 1000 km. Below 1000 km the viscosity of the lower-mantle for all 3 families is larger than that in the upper mantle. These results corroborate the complexity of the mantle viscosity profile between 660 and 1200 km, which would have important ramifications on flows between the upper and lower mantle. ¿ American Geophysical Union 1996