  We consider the equation of state of QCD at high density and zero temperature
in perturbation theory to first order in the coupling constant $\alpha_s$. We
compute the thermodynamic potential including the effect of a non-vanishing
mass for the strange quark and show that corrections are sizable.
Renormalization group running of the coupling and the strange quark mass plays
a crucial role. The structure of quark stars is dramatically modified.
