We argue that known systematics of hadron cross sections may cause different
particles to freeze out of the fireball produced in heavy-ion collisions at
different times. We find that a simple model with two freezeout points is a
better description of data than that with a single freezeout, while still
remaining predictive. The resulting fits seem to present constraints on the
late stage evolution of the fireball, including the tantalizing possibility
that the QCD chiral transition influences the yields at sqrt(S)=2700 GeV and
the QCD critical point those at sqrt(S)=17.3 GeV
