  I present here a concise summary of the preprint arXiv:0707.3024, written in
collaboration with A. Anisimov and P. Di Bari. There we discuss leptogenesis
when {\em CP} violation stems exlusively from the Dirac phase in the PMNS
mixing matrix. Under this assumption it turns out that the situation is very
constrained when a hierarchical heavy right-handed (RH) neutrino spectrum is
considered: the allowed regions are small and the final asymmetry depends on
the initial conditions. On the other hand, for a quasi-degenerate spectrum of
RH neutrinos, the {\em CP} asymmetry can be enhanced and the situation becomes
much more favorable, with no dependence on the initial conditions.
Interestingly, in the extreme case of resonant leptogenesis, in order to match
the observed baryon asymmetry of the Universe, we obtain a lower bound on \sin
\q_{13} which depends on the lightest active neutrino mass m_1.
