[en] The analytical solutions of Paper I are generalized using the self-consistent field method. These prolate models are constructed using only two integrals of motion, the energy (E) and the angular momentum about the axis of symmetry, (L/sub z/). They are the first models with flattening greater than E4 which possess elliptical isophotes and realistic density profiles. The singularity in the surface brightness which characterized the models of Paper I has been removed by smoothing the extreme suppression of L/sub z/. The new models (like those of Paper I) still show a sharp rise in the velocity dispersion at the center. This feature is due to the strongly anisotropic velocity dispersions, rather than the existence of a supermassive object