  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 $\left[U(3)\right]^5\otimes {\mathcal
O}(3)$ 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. The scheme
presented here could be tested in the near future via neutrino-less double beta
decay and cosmological measurements.
