We present an alternative method for determining the fluid motion immediately beneath the core-mantle boundary, based on solving the full nonlinear core motions problem. We use this method to examine three dynamical hypotheses about the flow: the steady motions hypothesis; the geostrophic hypothesis; and the toroidal flow hypothesis. We obtain better fits to the field with the toroidal flows than with geostrophic flows, casting considerable doubt on the validity of the geostrophic hypothesis. Additionally, we find some indication that failure of the frozen-flux approximation, a concomitant assumption, may be a serious obstacle to obtaining reliable maps of the core fluid flow. ¿ American Geophysical Union 1988