We study analytically and numerically the bounds imposed by the electroweak precision tests on a minimal composite Higgs model. The model is based on spontaneous SO(5) -> SO(4) breaking, so that an approximate custodial symmetry is preserved. The Higgs arises as a pseudo-Goldstone boson at a scale below the electroweak symmetry breaking scale. We show that one can satisfy the electroweak precision constraints without much fine-tuning. This is the case if the left-handed top quark is fully composite, which gives a mass spectrum within the reach of the LHC. However a composite top quark is strongly disfavored by flavor physics. The alternative is to have a singlet top partner at a scale much lighter than the rest of the composite fermions. In this case the top partner would be light enough to be produced significantly at the LHC.