  We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants
$g_{2}$ and $g_{3}$ 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
$R\simeq 0.8$. 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.
