  We perform an O(alpha_s^2) perturbative calculation of the equation of state
of cold but dense QCD matter with two massless and one massive quark flavor,
finding that perturbation theory converges reasonably well for quark chemical
potentials above 1 GeV. Using a running coupling constant and strange quark
mass, and allowing for further non-perturbative effects, our results point to a
narrow range where absolutely stable strange quark matter may exist. Absent
stable strange quark matter, our findings suggest that quark matter in compact
star cores becomes confined to hadrons only slightly above the density of
atomic nuclei. Finally, we show that equations of state including quark matter
lead to hybrid star masses up to M~2M_solar, in agreement with current
observations. For strange stars, we find maximal masses of M~2.75M_solar and
conclude that confirmed observations of compact stars with M>2M_solar would
strongly favor the existence of stable strange quark matter.
