  The discrete non-Abelian symmetry $A_4$, valid at some high-energy scale,
naturally leads to degenerate neutrino masses, without spoiling the hierarchy
of charged-lepton masses. Realistic neutrino mass splittings and mixing angles
(one of which is necessarily maximal and the other large) are then induced
radiatively in the context of softly broken supersymmetry. The quark mixing
matrix is also calculable in a similar way. The mixing parameter $U_{e3}$ is
predicted to be imaginary, leading to maximal CP violation in neutrino
oscillations. Neutrinoless double beta decay and $\tau \to \mu \gamma$ should
be in the experimentally accessible range.
