  We present multi-frequency VLBA observations of PMN J1632-0033, one of the
few gravitationally lensed quasars suspected of having a central ``odd'' image.
The central component has a different spectral index than the two bright quasar
images. Therefore, either the central component is not a third image, and is
instead the active nucleus of the lens galaxy, or else it is a third image
whose spectrum is inverted by free-free absorption in the lens galaxy. In
either case, we have more constraints on mass models than are usually available
for a two-image lens, especially when combined with the observed orientations
of the radio jets of the two bright quasars. If there is no third quasar image,
the simplest permitted model is a singular isothermal sphere in an external
shear field: beta=2.05^{+0.23}_{-0.10}, where rho(r) \propto r^{-beta}. If the
central component is a third image, a hypothesis which can be tested with
future high-frequency observations, then the density distribution is only
slightly shallower than isothermal: beta=1.91 +/- 0.02. We also derive limits
on the size of a constant-density core, and the break radius and exponent of an
inner density cusp.
