  In the context of the minimal supersymmetric seesaw model, the CP-violating
neutrino Yukawa couplings might induce an electron EDM. The same interactions
may also be responsible for the generation of the observed baryon asymmetry of
the Universe via leptogenesis. We identify in a model-independent way those
patterns within the seesaw models which predict an electron EDM at a level
probed by planned laboratory experiments and show that negative searches on
\tau-> e \gamma decay may provide the strongest upper bound on the electron
EDM. We also conclude that a possible future detection of the electron EDM is
incompatible with thermal leptogenesis, even when flavour effects are accounted
for.
