The role of decisions made by machine learning algorithms in our lives is ever increasing. In reaction to this phenomenon, the European General Data Protection Regulation establishes that citizens have the right to receive an explanation on automated decisions affecting them. For explainability to be scalable, it should be possible to derive explanations in an automated way. A common approach is to use simpler, more intuitive decision algorithms to build a surrogate model of the black-box model (for example a deep learning algorithm) used to make a decision. Yet, there is a risk that the surrogate model is too large for it to be really comprehensible to humans. We focus on explaining black-box models by using decision trees of limited size as a surrogate model. Specifically, we propose an approach based on microaggregation to achieve a trade-off between comprehensibility and representativeness of the surrogate model on the one side and privacy of the subjects used for training the black-box model on the other side.