We derive the single-mode, mean-field equations for spherical-shell convection with variable viscosity and compressibility included. Core-mantle boundary (CMB) topography produced by whole mantle convection is computed for various rheologies and different thermal boundary conditions at CMB. Results for long-wavelength undulations show the extreme sensitivity of these signatures to rheological and equation of state parameters. In order to obtain excess ellipticity of about 1 km, the activation energy and volume in the lower mantle should be low and the temperatues at CMB around 4,500 K, in accord with recent experimental findings. ¿ American Geophysical Union 1987