Since utterance verification (UV) may be treated as a two-class classification problem, it may be improved with discriminative training such as minimum verification error training or minimum verification error rate training. However, since in practice, one usually has to pick a specific false-acceptance or false-rejection rate for one's system, it is more desirable to optimize UV performance at a particular operating point. In this letter, we show that further improvement can be achieved by treating UV at a specific operating point as a constrained optimization problem