The seismically observed topography on the core-mantle boundary (CMB) and the velocities of the surface tectonic plates together constitute important observational constraints on viscous flow models of the Earth's mantle. We show here that the CMB deflections inferred by Morelli and Dziewonski (1987) may be explained in terms of a simple model of whole-mantle convection and in the process we provide a new method for inferring the penetration depths of subducted slabs. ¿ American Geophysical Union 1989