  The right-handed neutrinos within the type-I seesaw mechanism can induce
large radiative corrections to the Higgs mass, and naturalness arguments can
then be used to set limits on their mass scale and Yukawa couplings. Driven by
minimality, we consider the presence of two degenerate right-handed neutrinos.
We compare the limits from naturalness with the ones from the stability of the
electroweak vacuum and from lepton flavor violation. Implications from
neutrinoless double beta decay are also discussed and renormalization effects
for the light neutrino parameters are presented. Adding small perturbations to
the degenerate heavy neutrino spectrum allows for successful leptogenesis.
