Low-resistivity p-type ZnSe is difficult to make. This has been associated with the equilibrium thermodynamics of self-compensation of the p-type dopant by donor-like Se vacancies. We suggest that the bulk Se vacancy concentration can be vastly reduced by positioning the surface Fermi level near the conduction-band edge during the low-temperature epitaxial growth of p-doped ZnSe. This procedure is expected to minimize the equilibrium Se vacancy concentration at the surface, leading to a much lower than equilibrium Se vacancy concentration in the bulk. Experiments which could test this concept include liquid phase epitaxy growth of ZnSe from As or Li doped low work function melts such as Sn, and As doping during molecular beam epitaxy growth of ZnSe on (111)A surfaces.