A new reality in the southern areas of Tel-Aviv was created by negative social mobility. As a result, the variance in pupils' qualifications within each class, at high schools, was enlarged. One implication was that teachers' ability to advance pupils, who were able to reach a high level of knowledge, was weakened. The project for fostering the more gifted among socially disadvantaged adolescents has four main components: (1) Mastery of Mathematics and English at the basic level required by the university; (2) developing excellence in selected areas, as a means to enhance self-esteem and become acquainted with advanced subject matters; (3) peer group, to support social matriculation; and (4) developing capacity for critical thinking. Identification of the gifted is made by La. test, teacher's evaluations and reported self motivation. The main goal of the project is to encourage pupils' willingness and capacity to continue in academically oriented high schools and universities. Aside from dilemmas about creating and maintaining such project, preliminary results of evaluation research are reported.