  In a recent paper, we showed that tree level up-down unification of fermion
Yukawa couplings is a natural consequence of a large class of supersymmetric
models. They can lead to viable quark masses and mixings for moderately large
values of $\tan\beta$ with interesting and testable predictions for CP
violation in the hadronic sector. In this letter, we extend our discussion to
the leptonic sector focusing on one particular class of these models, the
supersymmetric left-right model with the seesaw mechanism for neutrino masses.
We show that fitting the solar and the atmospheric neutrino data considerably
restricts the Majorana-Yukawa couplings of the leptons in this model and leads
to predictions for the decay $\tau\to \mu +\gamma$, which is found to be
accessible to the next generation of rare decay searches. We also show that the
resulting parameter space of the model is consistent with the requirements of
generating adequate baryon asymmetry through lepton-number violating decays of
the right-handed neutrino.
