  The idea of naturalness, as originally conceived, refers only to the finite
renormalization of the Higgs boson mass induced by the introduction of heavier
states. In this respect, naturalness is still a powerful heuristic principle in
model building beyond the standard model whenever new massive states are
coupled to the Higgs field. The most compelling case is provided by the
generation of neutrino masses. In this paper we confront this problem from a
new perspective. The right-handed sector responsible for the seesaw
mechanism---which introduces a large energy threshold above the electroweak
scale---is made supersymmetric to comply with naturalness while the standard
model is left unchanged and non-supersymmetric. Cancellations necessary to the
naturalness requirement break down only at two loops, thus offering the
possibility to increase the right-handed neutrino mass scale up to one order of
magnitude above the usual values allowed by naturalness. If also the weak boson
sector of the standard model is made supersymmetric, cancellations break down
at three loops and the scale of new physics can be further raised. In the
type-I seesaw, this implementation provides right-handed neutrino masses that
are natural and at the same time large enough to give rise to baryogenesis (via
leptogenesis). The model contains a dark matter candidate and distinctive new
physics in the leptonic sector.
