[en] It is pointed out that the Higgs potentials in certain Yang-Mills-Higgs theories are natural in the sense that they can be derived by dimensionally reducing pure Yang-Mills theories defined in more than four space-time dimensions. In particular, when the symmetry group of the space of extra dimensions is subgroup of the initial gauge group, then the Higgs potential can be given a purely group theoretic interpretation. An interesting class of grand-unified-like models with Higgs potentials of this type can be derived using the exceptional group E₈ initial gauge group. One property of these models is that they are characterized by very few arbitrary parameters, neverhteless, a hierarchy of gauge symmetry breaking is still possible. (orig.)