  We develop a robust method to model quadruply lensed quasars, relying heavily
on the work of Witt (1996), who showed that for elliptical potentials, the four
image positions, the source, and the lensing galaxy lie on a right hyperbola.
For the singular isothermal elliptical potential, there exists a complementary
ellipse centered on the source which also maps through the four images, with
the same axis ratio as the potential but perpendicular to it. We first solve
for Witt's hyperbola, reducing the allowable space of models to three
dimensions. We then obtain the best fitting complementary ellipse. The simplest
models of quadruple lenses require seven parameters to reproduce the observed
image configurations, while the four positions give eight constraints. This
leaves us one degree of freedom to use as a figure of merit. We applied our
model to 29 known lenses, and include their figures of merit. We then modeled
100 random quartets. A selection criterion that sacrifices 20% of the known
lenses can exclude 98% of the random quartets.
