Abstract: 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 -> X-s gamma) to constrain the parameter space of a generic minimal supersymmetric standard model (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 tool 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 have the potential to render this bound obsolete in the near future.