  There exist lattice actions which give cut--off independent physical
predictions even on coarse grained lattices. Rotation symmetry is restored, the
spectrum becomes exact and, in addition, the classical equations have scale
invariant instanton solutions. This perfect action can be made short ranged. It
can be determined by combining analytical calculations with numerical
simulations on small lattices. We illustrate the method and the benefits on the
$d=2$ non--linear $\sigma$--model.
