  We present a detailed analysis of the skew-scattering contribution to the
spin Hall conductivity using an extended version of the resonant scattering
model of Fert and Levy [Phys. Rev. Lett. {\bf 106}, 157208 (2011)]. For $5d$
impurities in a Cu host, the proposed phase shift model reproduces the
corresponding first-principles calculations. Crucial for that agreement is the
consideration of two scattering channels related to $p$ and $d$ impurity
states, since the discussed mechanism is governed by a subtle interplay between
the spin-orbit and potential scattering in both angular-momentum channels. It
is shown that the potential scattering strength plays a decisive role for the
magnitude of the spin Hall conductivity.
