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