We have attempted to infer details of the viscosity structure in the top 1000 km of the mantle from the geoid and tomographic structure beneath the oceans. In order to eliminate the gravity signal from problematic masses located below the subduction zones and the continents, we have considered only the intermediate degrees of the oceanic geoid (ℓ = 12-25). A genetic algorithm has been used to determine the family of viscosity models which give the best correlation with the observed geoid. Our inversion clearly identifies the asthenosphere just below the lithosphere and also confirms the viscosity increase in the lower mantle predicted by previous inferences, but suggests that the main viscosity jump occurs at a depth of about 1000 km and not at the usually stated 660-km boundary. Somewhere in the depth range of 400-1000 km, a low viscosity zone may exist where the viscosity decreases to a value comparable with the asthenosphere. Existence of such a low viscosity zone is supported by recent analysis of deep mantle anisotropy which favours a flow pattern with a strong horizontal component in the top part of the lower mantle. Unfortunately, the resolution of the inversion as well as the quality of recent seismic tomographic models are not sufficient to localize the depth and to come up with a higher accuracy for the viscosity of this low viscosity channel.