[en] We analyze the implications of electroweak and strong coupling unification in a very general class of models extending the minimal supersymmetric standard model in 4 + p dimensions (p ≥ 0). In general, electroweak precision data require the presence of large extra dimensions (low compactification scales, M_c) and/or low unification scale, M_U. In particular, the actual experimental value of the strong coupling at M_Z imposes an upper bound on the compactification and unification scales. In four-dimensional theories (M_c congruent with M_U) with canonical hypercharge assignment we find M_U < or approx. 10⁹ GeV. In theories with extra dimensions (M_c < M_U) we find M_c 10⁷ GeV, for a supersymmetric spectrum at the TeV scale