  A one-flavour naturalness argument suggests that the Type I seesaw model
cannot naturally explain neutrino masses and the baryon asymmetry of the
Universe via hierarchical thermal leptogenesis. We prove that there is no way
to avoid this conclusion in a minimal three-flavour setup. We then comment on
the simplest ways out. In particular, we focus on a resolution utilising a
second Higgs doublet. Such models predict an automatically SM-like Higgs boson,
(maximally) TeV-scale scalar states, and low- to intermediate-scale
hierarchical leptogenesis with $10^3\text{ GeV}\lesssim M_{N_1}\lesssim
10^7\text{ GeV}$.
