  We analyze the structure of quark and lepton mass matrices under the
hypothesis that they are determined from a minimum principle applied to a
generic potential invariant under the $\left[SU(3)\right]^5\otimes \mathcal
O(3)$ flavor symmetry, acting on Standard Model fermions and right-handed
neutrinos. Unlike the quark case, we show that hierarchical masses for charged
leptons are naturally accompanied by degenerate Majorana neutrinos with one
mixing angle close to maximal, a second potentially large, a third one
necessarily small, and one maximal relative Majorana phase. Adding small
perturbations the predicted structure for the neutrino mass matrix is in
excellent agreement with present observations and could be tested in the near
future via neutrino-less double beta decay and cosmological measurements. The
generalization of these results to arbitrary sew-saw models is also discussed.
