the predicted range for $d_e$ and $d_\mu$ when the radiative corrections due to the right-handed neutrinos of the seesaw model and, possibly, the Higgs triplets of $SU(5)$ GUT provide the main source of CP violation and misalignment in slepton masses. This allows to extract many informations. If experimental searches could explore this range, one could obtain limits on the imaginary part of the relevant combination of neutrino Yukawa couplings. Moreover, the eventual discovery of a lepton EDM in this range might be interpreted as indirectly suggesting the existence of such a kind of fundamental particles which are too heavy to be more manifest. On the other hand, finding $d_e$ and/or $d_\mu$ above this predicted range would prove the existence of a source of CP (and likely also LF) violation other than these heavy states.

The pure seesaw case has been considered in Ref. [@ellis-1] - see also the related studies [@ellis-2; @ellis-n] on specific seesaw textures -, where it has been pointed out that threshold effects due to hierarchical right-handed neutrino masses enhance the radiatively-induced ${\cal I}m(A_{ii})$, $i=e,\mu,\tau$. By extensively reappraising this framework, we find that for $\tgb \gtrsim 10$ the amplitude with a LL RR double insertion - proportional 