  In this work, we use the results from Higgs searches in the $\gamma\gamma$
and $\tau\tau$ decay channels at LHC and indirect bounds as BR$(B \to X_s
\gamma)$ to constrain the parameter space of a generic MSSM Higgs sector. In
particular, we include the latest CMS results that look for additional Higgs
states with masses up to 1 TeV. We show that the $\tau \tau$ channel is the
best and most accurate weapon in the hunt for new Higgs states beyond the
Standard Model. We obtain that present experimental results rule out additional
neutral Higgs bosons in a generic MSSM below 300 GeV for any value of $\tan
\beta$ and, for instance, values of $\tan \beta$ above 30 are only possible for
Higgs masses above 600 GeV. ATLAS stored data has the potential to render this
bound obsolete in the near future.
