  We discuss the potential of Ginsparg-Wilson fermion simulations in the
epsilon-regime of chiral perturbation theory, regarding the determination of
the leading low energy constants of the effective chiral Lagrangian. It turns
out to be very hard to measure observables in the topologically trivial sector.
There a huge statistics would be required, due to the frequent occurrence of
very small eigenvalues. Moreover, contact with chiral perturbation theory is
only established if the physical volume of the system is sufficiently large.
