Mammography is the most effective method for breast cancer screening available today. However, the low positive predictive value of breast biopsy resulting from mammogram interpretation leads to approximately 70% unnecessary biopsies with benign outcomes. To reduce the high number of unnecessary breast biopsies, several computer-aided diagnosis (CAD) systems have been proposed in the last several years. These systems help physicians in their decision to perform a breast biopsy on a suspicious lesion seen in a mammogram or to perform a short term follow-up examination instead. We present two novel CAD approaches that both emphasize an intelligible decision process to predict breast biopsy outcomes from BI-RADS findings. An intelligible reasoning process is an important requirement for the acceptance of CAD systems by physicians. The first approach induces a global model based on decison-tree learning. The second approach is based on case-based reasoning and applies an entropic similarity measure. We have evaluated the performance of both CAD approaches on two large publicly available mammography reference databases using receiver operating characteristic (ROC) analysis, bootstrap sampling, and the ANOVA statistical significance test. Both approaches outperform the diagnosis decisions of the physicians. Hence, both systems have the potential to reduce the number of unnecessary breast biopsies in clinical practice. A comparison of the performance of the proposed decision tree and CBR approaches with a state of the art approach based on artificial neural networks (ANN) shows that the CBR approach performs slightly better than the ANN approach, which in turn results in slightly better performance than the decision-tree approach. The differences are statistically significant (p value < 0.001). On 2100 masses extracted from the DDSM database, the CRB approach for example resulted in an area under the ROC curve of A(z) = 0.89 +/- 0.01, the decision-tree approach in A(z) = 0.87 +/- 0.01, and the ANN approach in A(z) = 0.88 +/- 0.01.