  Completely natural electroweak symmetry breaking is easily achieved in
supersymmetric models if there is a SM-like Higgs boson, $h$, with $m_h\lsim
100\gev$. In the minimal supersymmetric model, such an $h$ decays mainly to
$b\anti b$ and is ruled out by LEP constraints. However, if the MSSM Higgs
sector is expanded so that $h$ decays mainly to still lighter Higgs bosons,
e.g. $h\to aa$, with $BR(h\to aa)>0.7$, and if $m_a<2m_b$, then the LEP
constraints are satisfied. In this letter, we show that in the next-to-minimal
supersymmetric model the above $h$ and $a$ properties (for the lightest CP-even
and CP-odd Higgs bosons, respectively) imply a lower bound on $BR(\Upsilon\to
\gam a)$ that dedicated runs at present (and future) $B$ factories can explore.
