We test exact and approximate Ginsparg-Wilson fermions with respect to thei
r chiral and scaling behavior in the 2-flavor Schwinger model. We first con
sider explicit approximate GW fermions in a short range, then we proceed to
their chiral correction by means of the "overlap formula", and finally we
discuss a numerically efficient perturbative chiral correction. In this way
we combine very good chiral and scaling properties with a relatively modes
t computational effort.