  New physics coupling to the Higgs sector of the Standard Model can lead to
dangerously large corrections to the Higgs mass. We investigate this problem in
the type II seesaw model for neutrino mass, where a weak scalar triplet is
introduced. The interplay of direct and indirect constraints on the type II
seesaw model with its contribution to the Higgs mass is analyzed. The focus
lies on testable triplet masses and (sub) eV-scale triplet vacuum expectation
values. We identify scenarios that are testable in collider and/or lepton
flavor violation experiments, while satisfying the Higgs naturalness criterion.
