Classification of rare events has many important data mining applications. Boosting is a promising meta-technique that improves the classification peformance of any weak classifier. So far, no systematic study has been conducted to evaluate how boosting performs for the task of mining rare classes. In this paper, we evaluate three existing categories of boosting algorithms from the single viewpoint of how they update the example weights in each iteration, and discuss their possible effect on recall and precision of the rare class. We propose enhanced algorithms in two of the categories, arid justib their choice of weight updating parameters theoretically. Using some specially designed synthetic datasets, we compare the capability of all the algorithms from the rare class perspective. The results support our qualitative analysis, and also indicate that our enhancements bring an extra capability for achieving better balance between recall and precision in mining rare classes.