  The Standard Model with a light Higgs provides a very accurate description of
the electroweak precision observables. The largest deviation between the
Standard Model predictions and the experimental measurements, the
forward-backward asymmetry of the bottom quark A{FB}^b, can be interpreted as
an indication of new physics at the TeV scale. The strong agreement between
theory and experiment in the branching fraction of the Z into b-quarks puts
strong constraints for new physics aiming to solve the A{FB}^b puzzle. We study
a class of natural composite Higgs models that can solve the A{FB}^b anomaly
reproducing the observed Rb as well as the top and bottom masses. We find that
the subgroup of the custodial symmetry able to protect Zb_L anti-b_L from large
corrections generated by the top sector play an important role if we want to
maintain naturalness in the composite sector. We make a thorough study of the
composite operators mixing with the b-quark, determine their embedding under
the global composite symmetry and the parameter space that lead to the correct
Zb anti-b couplings while keeping the top and bottom masses to their physical
values. We study the predictions for the spectrum of light fermionic resonances
and the corrections to Zt anti-t couplings in this scenario.
