The doping level in Cadmium Telluride (CdTe) is of the utmost importance for many applications. In this work, we have characterized CdTe crystals doped with Tl, Bi, or Yb as well as a crystal co-doped with Ge and Yb. The crystals were characterized using low-temperature Photoluminescence (PL), Positron Lifetime Spectroscopy (PLS), resistivity and a terahertz pump-probe technique that can determine carrier lifetimes. The properties of the crystals were also studied before and after a rapid thermal anneal (RTA) as well as after a longer conventional anneal. The results obtained using the various dopants vary widely. It will be shown, however, that the above mentioned dopants can form complexes with Cd vacancies (vacancy-impurity pairs). As a result, these Cd vacancies can play a key role in determining the resistivity and carrier lifetimes.