We present a method for designing efficient multigenic predictors with few probes and its application to the prediction of the response to preoperative chemotherapy in breast cancer. In this study, each DNA probe was regarded as an elementary predictor of the response to the chemotherapy and the probes which were selected performed a faithful sampling of the training dataset. In a first stage of the study, the prediction delivered by a multigenic predictor was that of the majority of the elementary predictions of its probes. For the data set at hand, the best majority decision predictor (MD predictor) had 30 probes. It significantly outperformed the best predictor designed on probes selected by p-value of a t-test (linear discriminant analysis on the 30 probes of least p-values). In a second stage, the majority decision was replaced by a support vector machine (SVM) acting as a linear classifier. With the same set of probes, the performances of the SVM predictor were slightly better for both training and testing. Moreover, the performances of the best MD predictor were achieved with 43% less probes by SVM predictors (17 probes). This downsizing of the predictors is an interesting property for their potential use in clinical routine and for modeling the biological mechanisms underlying the patient's response to the chemotherapy.