The group VA element P and the group IA elements Li and Na give rise to shallow acceptor centers in ZnTe and in CdTe. An analysis of the carrier concentration data for Li-doped ZnTe and P-doped ZnTe on the basis of a single-level acceptor and nondegenerate statistics indicates that P and Li produce shallow, hydrogenic-type acceptor levels in ZnTe. Annealing studies demonstrate that the shallow levels in Li-doped ZnTe and CdTe may be removed by heat treatment at 250°C for tens of hours. The concentrations of shallow acceptors in P-doped ZnTe and Na-doped ZnTe are relatively unchanged by the annealing procedure. The effective mass for holes in ZnTe as deduced from the Hall analysis is 0.36m, where m is the free-electron mass.