Fairness and interpretability are fundamental requirements for the development of responsible machine learning. However, learning optimal interpretable models under fairness constraints has been identified as a major challenge. In this paper, we investigate and improve on a state-of-the-art exact learning algorithm, called CORELS, which learns rule lists that are certifiably optimal in terms of accuracy and sparsity. Statistical fairness metrics have been integrated incrementally into CORELS in the literature. This paper demonstrates the limitations of such an approach for exploring the search space efficiently before proposing an Integer Linear Programming method, leveraging accuracy, sparsity and fairness jointly for better pruning. Our thorough experiments show clear benefits of our approach regarding the exploration of the search space.