  Adding a scalar triplet to the Standard Model is one of the simplest ways of
giving mass to neutrinos, providing at the same time a mechanism to stabilize
the theory's vacuum. In this paper, we revisit these aspects of the type-II
seesaw model pointing out that the bounded-from-below conditions for the scalar
potential in use in the literature are not correct. We discuss some scenarios
where the correction can be significant and sketch the typical scalar boson
profile expected by consistency.
