  In the Type I see-saw model, the naturalness requirement that corrections to
the electroweak $\mu$ parameter not exceed 1 TeV results in a rough bound on
the lightest right-handed neutrino mass, $M_{N_1}\lesssim 3\times 10^7$ GeV. In
this letter we derive generic bounds applicable in any three-flavour Type I
see-saw model. We find $M_{N_1}\lesssim 4\times 10^7$ GeV and $M_{N_2}\lesssim
7\times 10^7$ GeV. In the limit of one massless neutrino, there is no
naturalness bound on $M_{N_3}$ in the Poincare protected decoupling limit. Our
results confirm that no Type I see-saw model can explain the observed neutrino
masses and baryogenesis via hierarchical ($N_1$-, $N_2$-, or $N_3$-dominated)
thermal leptogenesis while remaining completely natural.
