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After classifying different extensions of the standard model according to their degree of naturality, I will present new class of perturbative models involving elementary scalars in which the theory simultaneously satisfies the Veltman conditions and is conformal at the classical level. I will show that such models are very constrained and thus highly predictive. Among the several examples, I will discuss a remarkably simple extension of the standard model in which the Higgs is predicted to have the experimental value of the mass equal to 126 GeV. The model also predicts the existence of one more standard model singlet scalar boson with a mass of 541 GeV and the Higgs self-coupling to emerge radiatively.