Cross-sectional shapes of many fish bodies are well approximated by ellipses. The simple elongated-body theory of balistiform locomotion was developed by Lighthill & Blake (1990) only in the limiting case when the axis ratio of the cross-section tends to zero. In that case they established that the movements of dorsal and anal fins, if attached to a rigid fish body of far greater depth, create fluid motions with substantially enhanced momentum. In this paper, standard conformal mappings are used to establish that enhancement is substantial also with elliptic cross-sections of arbitrary axis ratio, not only in balistiform locomotion with synchronous movement of two median fins but also in gymnotiform locomotion with movement of just a single (ventral) fin.