  We study the Higgs sector of supersymmetric models containing two Higgs
doublets with a light MSSM-like CP odd Higgs, $m_A \lesssim 10$ GeV, and $\tan
\beta \lesssim 2.5$. In this scenario all of the Higgses resulting from two
Higgs doublets: light and heavy CP even Higgses, $h$ and $H$, the CP odd Higgs,
$A$, and the charged Higgs, $H^\pm$, could have been produced at LEP or the
Tevatron, but would have escaped detection because they decay in modes that
have not been searched for or the experiments are not sensitive to. Especially
$H \to ZA$ and $H^\pm \to W^{\pm \star} A$ with $A \to c \bar c, \tau^+ \tau^-$
present an opportunity to discover some of the Higgses at LEP, the Tevatron and
also at B factories. Typical $\tau$- and $c$-rich decay products of all Higgses
require modified strategies for their discovery at the LHC.
