Absorber material with high and stable p-type doping that does not impede free carrier lifetime is the key component enabling efficiency and stability improvements in thin-film CdTe technology. To better understand the compensation mechanism and the metastable effects related to Cu acceptors, the most common p-type dopant in CdTe, i.e., a detailed kinetic model describing the behavior of intrinsic and Cu-related defects in this material, has been developed and applied for the first time. Migration and reactions of these point defects in single crystal CdTe have been investigated by solving diffusion-reaction equations in the time-space domain self-consistently with free carrier transport. The simulation results supported by reasonable match to experimental data have shed light on the nature of limited Cu incorporation (also known as the Cu solubility limits) and Cu self-compensation during the annealing and cooling processes.