As an effective method for evaluating efficiency, cross-efficiency evaluation has been widely used to assess the performance of Decision-Making Units (DMUs). However, non-uniqueness of the optimal weights problem reduces efficiency of this method. To address this problem, scholars have proposed using secondary goals and they have developed numerous models with this consideration. In this paper, two new secondary goal models are presented in order to further extend the above-mentioned existing models. The proposed altruism cross-efficiency model is speci cally applicable when the evaluated DMU cooperates with other DMUs, since it maximizes the peer-efficiency scores of other DMUs. On the other hand, the exclusiveness cross-efficiency model is utilized when the evaluated DMU is competing with other DMUs. This model minimizes the peer-efficiency scores of other DMUs. Compared with the existing approaches, our approach ensures that the peer-efficiencies generated by each DMU are maximized (or minimized) under the premise that the minimum (or maximum) peer-efficiency among the DMUs is maximized (or minimized). More importantly, our proposed algorithm guarantees the uniqueness of the optimal weights and the set of cross-efficiency scores. Two numerical examples were used to verify the effectiveness of the proposed model.