Higgs mass divergences require Standard Model extensions such as additional physics or fields. The divergences would be less unnatural for large Higgs masses. However, the electroweak precision tests (EWPT) indicate that the Standard Model Higgs is light (m(h) < 186 GeV). Nevertheless it is possible to increase the Higgs mass consistent with the EWPT. Here we review how this could be achieved introducing an extra Higgs doublet that has no couplings to leptons and quarks nor a vacuum expectation value. New scalar inert particles are obtained which are good dark matter candidates.