The Cd vacancy (VCd) and Te anti-site (TeCd) are two dominant defects in CdTe and CdZnTe alloys grown in Te-rich conditions. We examine the properties of these two intrinsic defects in Cd1-xZnxTe alloys with x<0.5 using first-principles calculations. It is shown that Cd vacancies become progressively more favourable with increasing Zn content, in contrast with Te anti-sites, which show the opposite behaviour, explaining the trend towards p-type conductivity in Cd1-xZnxTe.