  Lepton mixing can originate from the breaking of a flavor symmetry in
different ways in the neutrino and the charged lepton sector. We propose an
extension of this framework which allows to connect the mixing parameters with
masses, and more precisely, with certain types of degeneracy of the neutrino
mass spectrum. We obtain relations between the mixing parameters for the cases
of partial degeneracy, m1 = m2, and complete degeneracy, m1 = m2 = m3. These
relations determine also the Majorana phases. It is shown that relatively small
corrections to these lowest order results can produce the required mass
splitting and modify the mixing without significant changes of the other
symmetry results.
