  The Minimal Supersymmetric Standard Model contains in general sources of tau
lepton flavour violation which induce the rare decays tau --> mu gamma and tau
--> e gamma. We argue in this paper that the observation of both rare processes
would imply a lower bound on the radiative muon decay of the form BR(mu --> e
gamma) > C BR(tau --> mu gamma) BR(tau --> e gamma). We estimate the size of
the constant C without specifying the origin of the tau flavour violation in
the supersymmetric model and we discuss the implications of our bound for
future searches of rare lepton decays. In particular, we show that, for a wide
class of models, present B-factories could discover either tau --> mu gamma or
tau --> e gamma, but not both. We also derive for completeness the constant C
in the most general setup, pursuing an effective theory approach.
