  We apply different types of overlap operators in quenched QCD simulations to
compute the zero mode contribution to the pseudo-scalar correlator. In
particular we use the conventional Neuberger Dirac operator and the overlap
hypercube Dirac operator. Confronting our data with the analytical predictions
by Chiral Perturbation Theory we evaluate the pion decay constant and the
parameter \alpha of the quenched chiral Lagrangian.
