The equation of state for matter with energy density above2x1014&hthinsp;g/cm3is parametrized with three regions, two with adiabatic equations of state and the third with a causal equation of state. Searching the parameter space under a stability constraint, we find the maximum mass for a non-rotating relativistic neutron star depends on the maximum allowed values of the adiabatic index parameters. The maximum mass as a function of adiabatic index can be rendered to good approximation by a rational quadratic. Selecting a generous upper bound on the adiabatic index, it appears very likely that the maximum mass is less than three solar masses. ©1999 American Institute of Physics.