Discrimination and segregation have become major societal concerns while the increasing use of algorithms in various domains raises interest in their fairness and transparency. In this context, this paper presents a new approach to improve fairness in supervised classification, built on previous work. The proposed method uses the maximum-entropic formulation of logistic regression allowing for the easeful addition of linear (fairness) constraints directly on the probabilistic outputs of the model. We investigate the particular case of fairness problems, but the same technique could be applied to other situations requiring linear constraints on the outputs. In addition, we introduce a fairness-aware stepwise selection technique that gradually reduces the number of features according to their impact on demographic parity to further decrease discrimination. Experiments on five different datasets and comparisons with two competing models show that the proposed approach significantly reduces discrimination in terms of demographic parity, as well as in terms of two new measures of fairness described in this paper (the area under the demographic parity curve, and the F1 demographic parity) while maintaining a high level of accuracy on the investigated datasets.