Statler (1987) demonstrated that self-consistent triaxial models with the perfect density law could be constructed for virtually any choice of axis ratios. His experiments are repeated here using triaxial mass models based on Jaffe's density law, which has a central density that diverges as 1/r^2, similar to what is observed in low-luminosity elliptical galaxies. Most of the boxlike orbits are found to be stochastic in these models. Because timescales for chaotic mixing are generally shorter than a galaxy lifetime in triaxial models with strong cusps, and because fully-mixed stochastic orbits have shapes that are poorly suited to reproducing a triaxial figure, only the regular orbits are included when searching for self-consistent solutions. As a result of the restriction to regular orbits, self-consistent solutions are found only for mass models with a modest range of shapes, either nearly oblate, nearly prolate or nearly spherical. This result may explain in part the narrow range of elliptical galaxy properties.

10 Latex pages, 5 Postscript figures, uses aastex, epsf.sty. Submitted to The Astrophysical Journal, January 1997