As a model for nonideal behavior in the equation of state of QCD at high density, we consider cold quark matter in perturbation theory [E.S. Fraga, R.D. Pisarski and J. Schaffner-Bielich, PRD63, 121702 (2001); NPA702, 217 (2002)]. For almost twenty years the effects of a nonzero strange quark mass on the equation of state of cold and dense QCD were considered to be negligible (less than 5%), thereby yielding only minor corrections to the mass-radius diagram of compact stars. By computing the thermodynamic potential to first order in alpha_s, and including the effects of the renormalization group running of the coupling and strange quark mass, we show that the corrections can be very large (up to 25%), and dramatically affect the structure of compact stars, as can be seen from the modifications of the mass-radius diagram [E.S. Fraga and P. Romatschke [PRD71, 105014 (2005)].