Although neural networks and support vector machines (SVMs) are the traditional predictors for the classification of complex problems, these opaque paradigms cannot explain the logic behind the discrimination process. Therefore, within the quite unexplored area of evolutionary algorithms opening the SVM decision black box, the paper appoints a cooperative coevolutionary (CC) technique to extract discriminative and compact class prototypes following a SVM model. Various interactions between the SVM and CC are considered, while many experiments test three decisive hypotheses: fidelity to the SVM prediction, superior accuracy to the CC classifier alone and a compact and comprehensive resulting output, achieved through a class-oriented form of feature selection. Results support the hybridization by statistically and visually demonstrating its advantages.