In this talk I first show why the minimal three-flavour Type I see-saw model cannot explain the observed neutrino masses and the baryon asymmetry of the universe via hierarchical thermal leptogenesis without ceding naturalness. I then discuss how this conclusion can be avoided by adding a second Higgs doublet with tanβ ≳3. These models predict a SM-like Higgs boson, TeV-scale scalar states, and low to intermediate-scale hierarchical leptogenesis with 10^3 GeV ≲ M_{N_1} ≲ 10^8 GeV.