We prove that taking correctly into account the lepton flavour dependence of
the CP asymmetries and washout processes, it is possible to obtain successful
thermal leptogenesis from the decays of the second right-handed neutrino. The
asymmetries in the muon and tau-flavour channels are then not erased by the
inverse decays of the lightest right-handed neutrino, N_1. In this way, we
reopen the possibility of ``thermal leptogenesis'' in models with a strong
hierarchy in the right-handed Majorana masses that is typically the case in
models with up-quark--neutrino Yukawa unification.Comment: 5 pages, no figures. References added, referencing correcte