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We employ Data Envelopment Analysis, to estimate efficiency scores for Portuguese public universities. The input measures are constructed from the number of teachers and from universities' spending while the output measures are based on the undergraduate success rate and on the number of doctoral dissertations. Using frontier analysis we are able to separate universities that might qualify, as performing well from those where some improvement might be possible. This could imply a better allocation by the universities of the usually scarce public financial resources available to tertiary education.