We consider the extension of the standard model by a complex scalar triplet field, which occurs naturally in several models of leptogenesis and the seesaw mechanism for neutrino mass generation, in the context of ameliorating the fine-tuning problem of the fundamental scalars through the Veltman condition, i.e. by demanding the sum of the quadratically divergent corrections to vanish (or be at a reasonable level) by virtue of some possible symmetry of the underlying theory. We show that it is possible to cancel all the scalar one-loop quadratic divergences, and hence obtain a viable solution for the fine-tuning problem, while satisfying the electroweak precision observables, including the ρ parameter, and successfully generating the neutrino masses. The stability of the scalar potential puts important constraints on the model. © 2014 American Physical Society.