  A complete analysis of the electroweak precision observables is performed
within a recently proposed minimal composite Higgs model, realized as a
5-dimensional warped compactification. In particular, we compute Z->bb and the
one-loop correction to the rho parameter. We find that oblique data can be
easily reproduced without a significant amount of tuning in the parameters of
the model, while Z->bb imposes a stronger constraint. As a consequence of the
latter, some of the new fermionic resonances must have mass around 4 TeV, which
corresponds to an electroweak fine tuning of a few percent. Other resonances,
such as Z', can be lighter in sizeable portions of the parameter space. We
discuss in detail the origin of the Z->bb constraint and we suggest several
possible avenues beyond the minimal model for weakening it.
