  We show that a subgroup of the custodial symmetry O(3) that protects delta
rho from radiative corrections can also protect the Zbb coupling. This allows
one to build models of electroweak symmetry breaking, such as Higgsless, Little
Higgs or 5D composite Higgs models, that are safe from corrections to Z-> bb.
We show that when this symmetry protects Zbb it cannot simultaneously protect
Ztt and Wtb. Therefore one can expect to measure sizable deviations from the SM
predictions of these couplings at future collider experiments. We also show
under what circumstances Zb_R b_R can receive corrections in the right
direction to explain the anomaly in the LEP/SLD forward-backward asymmetry
A^b_{FB}.
