Positron states at pure monovacancies and divacancies and vacancy-phosphorus pairs in Si as well as at As vacancies and As-vacancy–As-antisite pairs in GaAs are calculated. The dependence of the positron lifetime on the lattice relaxation around the defects is studied, and the effects related to the screening of positrons are discussed. The calculations are based on superimposing free atoms. The ability of the method to describe positron states at charged defects is demonstrated.Peer reviewe