  It is a common believe that, if the Tri-bimaximal mixing (TBM) pattern is
explained by vacuum alignment in an A(4) model, only a very small reactor
angle, say \theta_{13} \sim \lambda^2_C being \lambda_C \equiv \theta_C the
Cabibbo angle, can be accommodated. This statement is based on the assumption
that all the flavon fields acquire VEVs at a very similar scale and the
departures from exact TBM arise at the same perturbation level. From the
experimental point of view, however, a relatively large value \theta_{13} \sim
\lambda_C is not yet excluded by present data. In this paper, we propose a
Seesaw A(4) model in which the previous assumption can naturally be evaded. The
aim is to describe a \theta_{13} \sim \lambda_C without conflicting with the
TBM prediction for \theta_{12} which is rather close to the observed value (at
\lambda^2_C level). In our model the deviation of the atmospherical angle from
maximal is subject to the sum-rule: \sin ^2 \theta_{23} \approx 1/2 +
\sqrt{2}/2 \sin \delta \cos \theta_{13} which is a next-to-leading order
prediction of our model.
