Though the combined data from high-z Type Ia SNe and from CMB
anisotropies strongly favour a significant cosmological constant,
statistics from gravitational lensing have historically produced a
strong upper bound on 
. The number of lensed quasars
observed is sensitive to the value of , and several
investigators (Fukugita & Turner 1991; Maoz & Rix 1993; Kochanek
1992, 1996; Falco et
al. 1998; but also see Cen et al. 1994 and Im et al. 1997) have found
that the low frequency of observed lensing events argues against a
dominant term, in particular Kochanek (1996,
hereafter K96) who finds a limit of 
at the
95% level for a flat universe.
Chiba & Yoshii (1999, hereafter CY), however, dispute this result by re-examining the parameters of gravitational lensing statistics. Such statistics depend upon two sets of parameters: those that describe the number density of lenses (drawn from the galaxy luminosity function) and those that describe the structure of each lens (drawn from the galaxy velocity dispersions and light profiles).