to $\tan^3 \beta$ - dominates over the one involving ${\cal I}m(A_{ii})$ - insensitive [^3] to $\tgb$ -, the exact ratio depending on the particular choice of supersymmetric mass parameters. We provide general expressions from which it is easy to recognize the model dependencies and which complete previous analyses. Lepton EDMs are then strongly enhanced in models with large $\tan \beta$. To see how close experiments are getting to the seesaw induced lepton EDMs range, we compare the upper estimates for the radiatively-induced misalignments and CP phases with the corresponding present and planned experimental limits collected in [@ms1].

The range for a seesaw-induced $d_\mu$ turns out to be quite far from present searches and, in particular, its eventual discovery above $10^{-23}$ e cm would prove the existence of a source of CP violation other than the neutrino Yukawa couplings. On the contrary, the present sensitivity to $d_e$ explores the seesaw-induced range in models with large $\tgb$ and small R-slepton masses, say $m_R$ around $100-200$ GeV. The planned improvements for $d_e$ would allow to test also models with $m_R$ up to the TeV region and moderate $\tgb$. When present or planned experimental limits turns out to overlap with these allowed ranges, bounds 