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 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 the hierarchical heavy RH neutrino spectrum, 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 motivation for models with degenerate heavy neutrino spectrum.