  We discuss the possibility of discriminating between different supersymmetric
see-saw models by improving the experimental sensitivity to charged lepton
flavour violating processes. Assuming a hierarchical neutrino mass spectrum, we
classify realistic see-saw models according to how the hierarchy Delta
m^2_{sun} << Delta m^2_{atm} is generated, and study the predictions of each
class for the branching ratios of tau -> mu gamma and mu -> e gamma. The
process tau -> mu gamma is found to be a particularly promising tool to probe
the fundamental see-saw parameters, and especially to identify the origin of
the large atmospheric mixing angle. Predictions for mu -> e gamma are more
model-dependent. We point out that, even with an improvement of the
experimental sensitivities by three orders of magnitude, both tau -> mu gamma
and mu -> e gamma could escape detection in models where Delta m^2_{atm} is
determined by one of the lightest right-handed neutrinos.
