  In supersymmetric models with a long-lived stau being the lightest Standard
Model superpartner, the stau abundance during primordial nucleosynthesis is
tightly constrained. Considering the complete set of stau annihilation channels
in the minimal supersymmetric Standard Model (MSSM) with real parameters for
scenarios in which sparticle coannihilations are negligible, we calculate the
decoupling of the lighter stau from the primordial plasma and identify
processes which are capable to deplete the resulting stau abundance
significantly. We find particularly efficient stau annihilation at the
resonance of the heavy CP-even Higgs boson and for a lighter stau with a
sizeable left-right mixing due to enhanced stau-Higgs couplings. Even within
the constrained MSSM, we encounter both effects leading to exceptionally small
values of the resulting stau abundance. Prospects for collider phenomenology
are discussed and possible implications of our findings are addressed with
emphasis on gravitino dark matter scenarios.
