  We discuss the conditions for a non-vanishing Dirac phase \delta and mixing
angle \theta_{13}, sources of CP violation in neutrino oscillations, to be
uniquely responsible for the observed matter-antimatter asymmetry of the
universe through leptogenesis. We show that this scenario, that we call
\delta-leptogenesis, is viable when the degenerate limit (DL) for the heavy
right-handed (RH) neutrino spectrum is considered. We derive an interesting
joint condition on \sin\theta_{13} and the absolute neutrino mass scale that
can be tested in future neutrino oscillation experiments. In the limit of
hierarchical heavy RH neutrino spectrum (HL), we strengthen the previous result
that \delta-leptogenesis is only very marginally allowed, even when the
production from the two heavier RH neutrinos is taken into account. An improved
experimental upper bound on \sin\theta_{13} and (or) an account of quantum
kinetic effects could completely rule out this option in the future. Therefore,
\delta-leptogenesis can be also regarded as a motivation for models with
degenerate heavy neutrino spectrum.
