  The analysis of hadronic interactions with effective field theory techniques
is complicated by the appearance of a large number of low-energy constants,
which are usually fitted to data. On the other hand, the large-$N_c$ limit
imposes natural short-distance constraints on these low-energy constants,
providing a parameter reduction. A Bayesian interpretation of the expected
$1/N_c$ accuracy allows for an easy and efficient implementation of these
constraints, using an augmented $\chi^2$. We apply this approach to the
analysis of meson-meson scattering, in conjunction with chiral perturbation
theory to one loop and coupled-channel unitarity, and show that it helps to
largely reduce the many existing ambiguities and simultaneously provide an
acceptable description of the available phase shifts.
