In this paper we present a detailed analysis of the Electroweak Precision Observables (EWPO) in composite Higgs models based on the coset $SO(5)/SO(4)$. In our study we include both the fermionic top partners and the spin-1 resonances and consider their possible interplay as well. In order to achieve calculability we use the assumptions of i) partial Ultra Violet Completion (PUVC) following arXiv:1109.1570 and, ii) absence of sizeable effects from physics above the cut-off. Apart from the EWPO, we also take into account the constraints from the top quark, $Z$ and the Higgs boson masses whenever they can be predicted in terms of the model parameters. After presenting our analytic results (often, in certain limits) and discussing their symmetry properties, we also perform detailed fits of the model parameters following the Bayesian approach. We show the posterior probability distributions of the parameters in various scenarios and provide with analytic understanding whenever possible. We find that in certain cases the EWPO allow the compositeness scale to lie well below $1$ TeV. Moreover, fermionic top partners of mass around $1$ TeV and spin-1 resonances of mass around $2-3$ TeV are consistent with the precision data.

Final version to appear in Nuclear Physics B