We show that the Doppler broadening of positron annihilation radiation can be used in the identification of vacancy defects in compound semiconductors. Annihilation of trapped positrons with surrounding core electrons reveals chemical information that becomes visible when the experimental backgorund is reduced by the coincidence technique. We also present a simple calculational scheme to predict the high-momentum part of the annihilation line. The utility of the method is demonstrated by providing results for vacancies in InP. In electron irradiated InP the isolated In and P vacancies are distinguished from each other by the magnitude of the core-electron annihilation. In heavily Zn-doped InP we detect a native vacancy defect and identify it to a P vacancy decorated by Zn atoms.Peer reviewe