We estimate the ratio R=g3/g2 of the critical coupling constants
g2 and g3 which are required to achieve binding of 2 or 3 bosons,
respectively, with a short-range interaction, and examine how this ratio
depends on the shape of the potential. Simple monotonous potentials give
R≃0.8. A wide repulsive core pushes this ratio close to R=1. On the
other hand, for an attractive well protected by an external repulsive barrier,
the ratio approaches the rigorous lower bound R=2/3. We also present results
for N=4 bosons, sketch the extension to N>4, and discuss various
consequences.Comment: 12 pages, RevTeX, 5 Figures in tex include