This paper proposes an efficient three-stage classifier for handwritten digit recognition based on NN (Neural Network) and SVM (Support Vector Machine) classifiers. The classification is performed by 2 NNs and one SVM. The first NN is designed to provide a low misclassification rate using a strong rejection criterion. It is applied on a small set of easy to extract features. Rejected patterns are forwarded to the second NN that uses additional, more complex features, and utilizes a wellbalanced rejection criterion. Finally, rejected patterns from the second NN are forwarded to an optimized SVM that considers only the "top k" classes as ranked by the NN. This way a very fast SVM classification is obtained without sacrificing the classifier accuracy. The obtained recognition rate is among the best on the MNIST database and the classification time is much better compared to the single SVM applied on the same feature set.