  We consider the extension of the Standard Model by a complex scalar triplet
field, which occurs naturally in several models of leptogenesis and see-saw
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 $\rho$ parameter, and successfully generating the neutrino
masses. The stability of the scalar potential puts important constraints on the
model.
