In minimal theories with extra spatial dimensions at scales mu(0) much lowe
r than the conventional GUT scale, unification can give too-large predictio
ns for alpha(3)(M-Z) given alpha(1)(M-Z) and alpha(2)(M-Z) as empirical inp
ut. We systematically study the effects of adding extra states above the co
mpactification scale on running of the gauge couplings and find several sim
ple examples that give unification where all alpha(i)(M-Z) are consistent w
ith low-energy data. We study both the supersymmetric and nonsupersymmetric
unification. (C) 1999 Published by Elsevier Science B.V. All rights reserv
ed.