The article is about a new Classifier System framework for classification tasks called BYP CS (for BaYesian Predictive Classifier System). The proposed CS approach abandons the focus on high accuracy and addresses a well-posed Data Mining goal, namely, that of uncovering the low-uncertainty patterns of dependence that manifest often in the data. To attain this goal, BYP CS uses a fair amount of probabilistic machinery, which brings its representation language closer to other related methods of interest in statistics and machine learning. On the practical side, the new algorithm is seen to yield stable learning of compact populations, and these still maintain a respectable amount of predictive power. Furthermore, the emerging rules self-organize in interesting ways, sometimes providing unexpected solutions to certain benchmark problems.