We perform an analysis of the Renormalization Group evolution of the couplings in an extension to the Standard Model which contains a real triplet in the Higgs sector. Insisting that the model remain valid up to 1 TeV allow us to map out the region of allowed mass for the Higgs bosons. We conclude that it is possible for there to be no light Higgs bosons without any otherwise dramatic deviation from the physics of the Standard Model. 1