  Quantitative estimates of lensing probabilities must be self-consistent. In
particular, for asymptotically isothermal models: (1) using the $(3/2)^{1/2}$
correction for the velocity dispersion overestimates the expected number of
lenses by 150\% and their average separations by 50\%, thereby introducing
large cosmological errors; (2) when a core radius is added to the SIS model,
the velocity dispersion must be increased; and (3) cross sections and
magnification bias cannot be separated when computing the lensing probability.
When we self-consistently calculate the effects of finite core radii in flat
cosmological models, we find that the cosmological limits are independent of
the core radius.
