  We simulate 3-flavour lattice QCD at finite quark-number chemical potential
mu in the phase-quenched approximation, close to the finite temperature
transition. Working close to the critical quark mass, we find no evidence for
the expected critical endpoint at small mu. We are performing further
simulations aimed at calculating the equation-of-state of this theory outside
of the superfluid domain, where its phase structure is expected to mimic the
full theory.
