One of the main causes of the unemployment in low-qualification socioeconomic sectors is the problem of asymmetry of information: firms ignore the true predisposition of the candidates to commit with the job, and facing such uncertainty, they deter from contracting personnel. Using an optimization model, based on the revelation principle for games of incomplete information, we deduce that the public system should offer to those candidates willing to commit salaries too high in order to distinguish them from other candidates. That is why the public system only offers low-commitment transitory jobs, leaving out of the intermediation system the unemployed people with the highest potential. As an alternative, we propose to implement a mixed public-private system, in which the public agencies would specialize on transitory jobs, and the private agencies on higher commitment jobs. In such a case, the salaries for the latter jobs would be realistic, so people with a high potential would participate in the intermediation system.