We demonstrate the impact that present lepton flavour and CP violation data - neutrino oscillations, baryon asymmetry of the universe, flavour violations in charged lepton decays and lepton electric dipole moments - have on supersymmetric seesaw theories by analysing the class of models based on a U(1) flavour symmetry. The fermion U(1) charges are determined to a large extent by the data, the flavour patterns being naturally defined through their choice. The selected models generically predict

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... mu -> e gamma within the reach of the projected experiments, which could be sensitive enough to exclude the whole class of them. By now, the present sensitivity to mu -> e gamma already provides stringent bounds on the contribution of the seesaw couplings to the lepton electric dipole moments.