Natural relations among physical observables in the neutrino mass matrix

We find all possible relations among physical observables arising from neutrino mass matrices that describe in a natural way the currently observed pattern (tan_23 and tan_12 large, dm^2_Sun/dm^2_Atm and tan_13 small) 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.