Undoped and doped CdTe wafers have been thermally annealed in Ga melt, or in Cd vapour or in a vacuum to eliminate Te precipitates from the volume of the wafers. The effect of annealing conditions on the transformation of Te precipitates has been studied by Raman scattering (RS) and cathodoluminescence (CL) techniques. The RS and CL spectra of the as-grown and annealed wafers are discussed in connection with the doping and native structural defects and residual impurities. The kinetics of elimination of Te precipitates was found to be similar in the undoped and doped wafers. The rate of elimination is the highest for the annealing in Ga melt. Precipitate-free wafers have been obtained by annealing in Ga melt at 600 degrees C for 24 h. Simultaneously with the elimination of Te precipitates, Ga melt causes the in-diffusion of Ga atoms into the wafers. This implies that annealing in Ga melt could be a superior procedure for the elimination of Te precipitates from CdTe wafers in which Ga doping is not important or is desired.