Most highly accurate predictive modeling techniques produce opaque models. When comprehensible models are required, rule extraction is sometimes used to generate a transparent model, based on the opaque. Naturally, the extracted model should be as similar as possible to the opaque. This criterion, called fidelity, is therefore a key part of the optimization function in most rule extracting algorithms. To the best of our knowledge, all existing rule extraction algorithms targeting fidelity use 0/1 fidelity, i.e., maximize the number of identical classifications. In this paper, we suggest and evaluate a rule extraction algorithm utilizing a more informed fidelity criterion. More specifically, the novel algorithm, which is based on genetic programming, minimizes the difference in probability estimates between the extracted and the opaque models, by using the generalized Brier score as fitness function. Experimental results from 26 UCI data sets show that the suggested algorithm obtained considerably higher accuracy and significantly better AUC than both the exact same rule extraction algorithm maximizing 0/1 fidelity, and the standard tree inducer J48. Somewhat surprisingly, rule extraction using the more informed fidelity metric normally resulted in less complex models, making sure that the improved predictive performance was not achieved on the expense of comprehensibility.