  We extend the results of [arXiv:1006.0207 [hep-lat]] by computing the
S-parameter at two loops in the perturbative region of the conformal window.
Consistently using the expression for the location of the infra-red fixed point
at the two-loop order we express the S-parameter in terms of the number of
flavors, colors and matter representation. We show that S, normalized to the
number of flavors, increases as we decrease the number of flavors. Our findings
support the conjecture presented in [arXiv:1006.0207 [hep-lat]] according to
which the normalized value of the S-parameter at the upper end of the conformal
window constitutes the lower bound across the entire phase diagram for the
given underlying asymptotically free gauge theory. We also show that the
non-trivial dependence on the number of flavors merges naturally with the
non-perturbative estimate of the S-parameter close to the lower end of the
conformal window obtained using gauge duality [arXiv:1007.0254 [hep-ph]]. Our
results are natural benchmarks for lattice computations of the S-parameter for
vector-like gauge theories.
