  We introduce the ``Sequential Empirical Bayes Method'', an adaptive
constrained-curve fitting procedure for extracting reliable priors. These are
then used in standard augmented-$\chi^2$ fits on separate data. This better
stabilizes fits to lattice QCD overlap-fermion data at very low quark mass
where {\it a priori} values are not otherwise known. Lessons learned (including
caveats limiting the scope of the method) from studying artificial data are
presented. As an illustration, from local-local two-point correlation
functions, we obtain masses and spectral weights for ground and first-excited
states of the pion, give preliminary fits for the $a_0$ where ghost states (a
quenched artifact) must be dealt with, and elaborate on the details of fits of
the Roper resonance and $S_{11}(N^{1/2-})$ previously presented elsewhere. The
data are from overlap fermions on a quenched $16^3\times 28$ lattice with
spatial size $La=3.2 {\rm fm}$ and pion mass as low as $\sim 180 {\rm MeV}$.
