A principled methodology for solving imbalanced binary classification problems has been recently introduced. It permits to obtain high performance designs avoiding the risks of degradation that other procedures suffer from. The corresponding paper Benítez-Buenache et al. (2019) shows evidence of these facts by applying direct versions, using just one of the possible rebalancing techniques and applying full rebalancing. In this contribution, we extend the above study for maximizing the performance of the resulting designs. To this end, we combine principled techniques in order to taking benefit from their different characteristics. The combination weights as well as the rebalance degree are selected by means of a simple (cross-validation) search. A number of experiments with different kinds of databases shows significant performance improvements. At the same time, the database characteristics that limit the performance improvements −such as small size and noisy samples− are detected. •Combining different (neutral) principled rebalancing techniques is proposed.•The combination degree and the rebalancing intensity are found by cross validation.•Extensive experiments support the effectiveness of the proposal.•Shallow and deep neural networks and ensembles are used in the experiments.•The database characteristics that reduce combinations performance are detected.