Abstract: A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum rules. One of these implies a lower bound on the effective neutrinoless double beta mass parameter, even for normal hierarchy neutrinos. Here we propose a new model based on the S-4 flavor symmetry that leads to the new neutrino mass sum rule and discuss how to generate a nonzero value for the reactor angle theta(13) indicated by recent experiments, and the resulting correlation with the solar angle theta(12).