  We show that a modification of a recently proposed model by Altarelli and
Feruglio with softly broken $A_4$ symmetry leads naturally to nonvanishing
$U_{e3}$ with $\theta_{13}\simeq 2^o - 4^o$. The observed mass squared
differences for solar and atmospheric neutrinos have been fitted without fine
tuning among model parameters. The predicted solar neutrino mixing angle is
brought down from the tri-bimaximal prediction to be in concordance with the
latest global analysis including experimental data from KamLAND and SNO.
