  We propose new techniques for the numerical implementation of the
overlap-Dirac operator, which exploit the physical properties of the underlying
theory to avoid nested algorithms. We test these procedures in the
two-dimensional Schwinger model and the results are very promising. These
techniques can be directly applied to QCD simulations. We also present a
detailed computation of the spectrum and the chiral properties of the Schwinger
model in the overlap lattice formulation.
