  We revisit leptogenesis in the minimal non-supersymmetric type I see-saw
mechanism with two right-handed (RH) neutrinos, including flavour effects and
allowing both RH neutrinos N_1 and N_2 to contribute, rather than just the
lightest RH neutrino N_1 that has hitherto been considered. By performing scans
over parameter space in terms of the single complex angle z of the orthogonal
matrix R, for a range of PMNS parameters, we find that in regions around z \sim
\pm \pi/2, for the case of a normal mass hierarchy, the N_2 contribution can
dominate the contribution to leptogenesis, allowing the lightest RH neutrino
mass to be decreased by about an order of magnitude in these regions, down to
M_1 \sim 1.3*10^11 GeV for vanishing initial N_2-abundance, with the numerical
results supported by analytic estimates. We show that the regions around z \sim
\pm \pi /2 correspond to light sequential dominance, so the new results in this
paper may be relevant to unified model building.
