The degree of predictive validity and the relationship with previous learning conditions were studied for measures used in admission procedures for upgrading courses in science and mathematics in Botswana, Lesotho, and Swaziland. School results, achievement tests, aptitude tests, and ability tests were evaluated for students leaving secondary school for courses preparatory to tertiary education. Admissions procedures in developing countries usually aim for maximum predictive validity and fair chances for those who have had insufficient opportunities to develop their potentials. The various measures showed decreasing variation among schools in this order: (1) school results; (2) achievement tests; (3) aptitude tests; and (4) ability tests. Aptitude and ability measures were characterized by lower predictive value. If equal chances for education were to be pursued for various groups of candidates, the psychometric analyses of this study seemed too narrow to solve the selection problem. Multidisciplinary research is an essential approach to studying selection procedures. Data are presented in table form. (SLD)