  The recent T2K and MINOS indications for a "large" theta_13 neutrino mixing
angle can be accommodated in principle by an infinite number of Yukawa flavour
structures in the seesaw model. Without considering any explicit flavour
symmetry, there is an instructive exercise one can do: to determine the
simplest flavour structures which can account for the data with a minimum
number of parameters, simply assuming these parameters to be uncorrelated. This
approach points towards a limited number of simple structures which show the
minimum complexity a neutrino mass model must generally involve to account for
the data. These basic structures essentially lead to only 4 relations between
the neutrino observables. We emphasize that 2 of these relations, |sin
theta_13|=(tan theta_23/cos delta)*(1-tan theta_12)/(1+tan theta_12) and |sin
theta_13| = sin theta_12 R^1/4, with R= Delta m^2_21/Delta m^2_32, have several
distinctive properties. First, they hold not only with a minimum number of
parameters, but also for complete classes of more general models. Second, any
value of theta_13 within the T2K and MINOS ranges can be obtained from these
relations by taking into account small perturbations. Third, they turn out to
be the pivot relations of models with approximate conservation of lepton
number, which allow the seesaw interactions to induce observable flavour
violating processes, such as mu -> e gamma and tau -> mu gamma. Finally, in
specific cases of this kind, these structures have the rather unique property
to allow a full reconstruction of the seesaw Lagrangian from low energy data.
