Automated Machine Learning (Auto-ML) methods search for the best classification algorithm and its best hyper-parameter settings for each input dataset. Auto-ML methods normally maximize only predictive accuracy, ignoring the classification model’s interpretability – an important criterion in many applications. Hence, we propose a novel approach, based on Auto-ML, to investigate the trade-off between the predictive accuracy and the interpretability of classification-model representations. The experiments used the Auto-WEKA tool to investigate this trade-off. We distinguish between white box (interpretable) model representations and two other types of model representations: black box (non-interpretable) and grey box (partly interpretable). We consider as white box the models based on the following 6 interpretable knowledge representations: decision trees, If-Then classification rules, decision tables, Bayesian network classifiers, nearest neighbours and logistic regression. The experiments used 16 datasets and two runtime limits per Auto-WEKA run: 5 h and 20 h. Overall, the best white box model was more accurate than the best non-white box model in 4 of the 16 datasets in the 5-hour runs, and in 7 of the 16 datasets in the 20-hour runs. However, the predictive accuracy differences between the best white box and best non-white box models were often very small. If we accept a predictive accuracy loss of 1% in order to benefit from the interpretability of a white box model representation, we would prefer the best white box model in 8 of the 16 datasets in the 5-hour runs, and in 10 of the 16 datasets in the 20-hour runs.