Many of the existing machine-learning approaches to speech summarization cast important sentence selection as a two-class classification problem and have shown empirical success for a wide variety of summarization tasks. However, the imbalanced-data problem sometimes results in a trained speech summarizer with unsatisfactory performance. On the other hand, training the summarizer by improving the associated classification accuracy does not always lead to better summarization evaluation performance. In view of such phenomena, we hence investigate two different training criteria to alleviate the negative effects caused by them, as well as to boost the summarizer's performance. One is to learn the classification capability of a summarizer on the basis of the pair-wise ordering information of sentences in a training document according to a degree of importance. The other is to train the summarizer by directly maximizing the associated evaluation score. Experimental results on the broadcast news summarization task show that these two training criteria can give substantial improvements over the baseline SVM summarization system.