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-Nc limit helps to impose natural short-distance constraints on these low-energy constants, providing a parameter reduction. A Bayesian interpretation of the expected 1/Nc accuracy allows for an easy and efficient implementation of these constraints, using an augmented χ2. 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.