  We introduce the ``Sequential Empirical Bayes Method'', an adaptive
constrained-curve fitting procedure for extracting reliable priors. These are
then used in standard augmented-chi-square fits on separate data. This better
stabilizes fits to lattice QCD overlap-fermion data at very low quark mass
where a priori values are not otherwise known. We illustrate the efficacy of
the method with data from overlap fermions, on a quenched $16^3\times 28$
lattice with spatial size La=3.2 fm and pion mass as low as $\sim$ 180 MeV.
