Ellipsoid ARTMAP (EAM) is an adaptive-resonance-theory neural network architecture that is capable of successfully performing classification tasks using incremental learning. EAM achieves its task by summarizing labeled input data via hyper-ellipsoidal structures (categories). A major property of EAM, when using off-line fast learning, is that it perfectly learns its training set after training has completed. Depending on the classification problems at hand, this fact implies that off-line EAM training may potentially suffer from over-fitting. For such problems we present an enhancement to the basic Ellipsoid ARTMAP architecture, namely Boosted Ellipsoid ARTMAP (bEAM), that is designed to simultaneously improve the generalization properties and reduce the number of created categories for EAM's off-line fast learning. This is being accomplished by forcing EAM to be tolerant about occasional misclassification errors during fast learning. An additional advantage provided by bEAM's desing is the capability of learning inconsistent cases, that is, learning identical patterns with contradicting class labels. After we present the theory behind bEAM's enhancements, we provide some preliminary experimental results, which compare the new variant to the original EAM network, Probabilistic EAM and three different variants of the Restricted Coulomb Energy neural network on the square-in-a-square classification problem.