  Recent observations of galaxy luminosity profiles and dark matter simulations
find luminosity and mass distributions characterized by central cusps rather
than finite core radii. We introduce and implement a set of cusped ellipsoidal
lens models which include limits similar to the Jaffe, Hernquist, \eta and NFW
models and apply them to the gravitational lenses APM 08279+5255 and B
1933+503. A successful model of APM 08279+5255 with its central, odd image
requires a very shallow cusp, $\gamma \ltorder 0.4$ where $\rho \propto
r^{-\gamma}$ as $r\to 0$, which is similar to a core rather than the favored $1
\ltorder \gamma \ltorder 2$ cusps. B~1933+503, by contrast, is well modeled
with a steep density cusp, $1.6 \ltorder \gamma \ltorder 2.0$.
