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In a concept learning problem, imbalances in the distribution of the data can occur either between the two classes or within a single class. Yet, although both types of imbalances are known to affect negatively the performance of standard classifiers, methods for dealing with the class imbalance problem usually focus on rectifying the between-class imbalance problem, neglecting to address the imbalance occuring within each class. The purpose of this paper is to extend the simplest proposed approach for dealing with the between-class imbalance problem--random re-sampling--in order to deal simultaneously with the two problems. Although re-sampling is not necessarily the best way to deal with problems of imbalance, the results reported in this paper suggest that addressing both problems simultaneously is beneficial and should be done by more sophisticated techniques as well.