Predictions of physical observables from minimal neutrino structures

We find all possible seesaw textures which can describe in a natural way the currently observed neutrino oscillation pattern in terms of a minimum number of parameters. Natural here means due only to the relative smallness (vanishing) of some parameters in the relevant lagrangian, without special relations or accidental cancellations among them. The corresponding predictions for the mixing angle theta_13 and the effective mass m_ee are given.