  The next-to-minimal supersymmetric model with a light doublet-like
  CP-odd Higgs boson and small $\tan \beta$ can satisfy all experimental limits
on Higgs bosons even with light superpartners. In these scenarios, the two
lightest CP-even Higgs bosons, $\hi$ and $\hii$, and the charged Higgs boson,
$\hp$, can all be light enough to be produced at LEP and yet have decays that
have not been looked for or are poorly constrained by existing collider
experiments. The channel $\hi\to \ai\ai$ (where $\ai$ is the lightest CP-odd
boson and has mass below $2m_b$) with $\ai\to \tau^+\tau^-$ or $2j$ is still
awaiting LEP constraints for $\mhi>86\gev$ or $82\gev$, respectively. LEP data
may also contain $\epem\to \hii\ai$ events where $\hii\to Z\ai$ is the dominant
decay, a channel that was never examined. Decays of the charged Higgs bosons
are often dominated by $H^\pm \to W^{\pm (\star)} \ai$ with $\ai \to gg,c \bar
c, \tau^+ \tau^-$. This is a channel that has so far been ignored in the search
for $t\to \hp b$ decays at the Tevatron. A specialized analysis might reveal a
signal. The light $\ai$ might be within the reach of $B$ factories via
$\Upsilon\to \gamma \ai$ decays. We study typical mass ranges and branching
ratios of Higgs bosons in this scenario and compare these scenarios where the
$\ai$ has a large doublet component to the more general scenarios with
arbitrary singlet component for the $\ai$.
