  We investigate the general group structure of gauge-Higgs unified models. We
find that a given embedding of the \sm\ gauge group will imply the presence of
additional light vectors, except for a small set of special cases, which we
determine; the arguments presented are independent of the compactification
scheme. For this set of models we then find those that can both accommodate
quarks and have a vanishing oblique T-parameter at tree-level. We show that
none of the resulting models can have $|\sw| \sim1/2 $ (the sine of the
weak-mixing angle) at tree-level and briefly discuss possible solutions to this
problem.
