Bathymetry and gravity data from four geophysical surveys along the 15¿--19 ¿S superfast spreading section of the East Pacific Rise are used to study formation of the axial topographic high. After removing a best fitting thermal model the averaged, residual, axial topography is ~265 m high and ~15 km wide. The residual gravity shows no evidence for shallow isostatic compensation of this topography suggesting deep-rooted compensation or dynamic support. Previous models postulate that the axial high is compensated by low densities in a zone of partial melting within the upper mantle. We model the physical properties of the lithosphere and asthenosphere required to match the residual gravity and bathymetry using a nonlinear inversion, assuming the high is uplifted by buoyancy forces from low-density mantle. Deep-rooted buoyancy forces cannot create a narrow axial high unless they occur in a low-viscosity conduit surrounded by high-viscosity mantle. This high-viscosity region could be created by depletion and extraction of all water during the melting process. We find that the viscosity of the asthenosphere beneath the melt conduit must also be lower than the viscosity of the residual mantle surrounding the conduit. Our most reasonable model has a viscosity of 1020 Pa s in the residual mantle surrounding a melt conduit which extends 50 km below the seafloor and a viscosity of 1016.6 Pa s in the asthenosphere below the melt conduit. The viscosity of the melt conduit must be about 1015 Pa s, or about 105 times lower than the surrounding residual mantle, with a density contrast equivalent to the retention of a small fraction of melt (5%). Because higher melt concentrations are probably required to create even small changes in viscosity and the viscosity of the undepleted mantle is probably higher than 1016.6 Pa s, we conclude that it is unlikely that the axial topographic high is formed by buoyancy forces in the crust and mantle. ¿ 1998 American Geophysical Union