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In this correspondence, an asymmetric version of the label switching technique to build binary classification ensembles is introduced. The new version presents one more design parameter, the degree of asymmetry, and, consequently, it is more flexible to adapt to the problem under study. In particular, asymmetric switching allows designs that resist to class imbalance. A Bayesian analysis serves to establish how to deal with datasets for carrying out a principled rebalancing, which can be combined with other principled procedures according to the relative advantages of asymmetric switching. A number of simple experiments support the low sensitivity to imbalance and the validity of the analysis for this method of constructing ensembles.