  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.
