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Typical digit recognizers classify an unknown digit pattern by computing its distance from the cluster centers in a feature space. The-nearest neighbor (KNN) rule assigns the unknown pattern to the class belonging to the majority of its neighbors. These and other traditional methods adopt a uniform rule irrespective of the "difficulty" of the unknown pattern. In this paper, we propose a methodology that has many salient aspects. First, the classification rule is dependent on the "difficulty" of the unknown sample. Samples "far" from the center, which tend to fall on the boundaries of classes are error prone and, hence, "difficult." An "overlapping zone" is defined in the feature space to identify such difficult samples. A table is precomputed to facilitate an efficient lookup of the class corresponding to all the points in the overlapping zone. The lookup function itself is defined by a modification of the KNN rule. By reassigning the error-prone samples, we actually redefine the class boundaries. A characteristic function defining the new boundaries is computed using the topology of the set of samples in the overlapping zones. Our two-pronged approach uses different classification schemes with the "difficult" and "easy" samples. This could enable potential improvement of a recognition system. We have tested this methodology on a large set (30 398) of handwritten digit images. The method described in this paper has improved the performance of the gradient structural concavity (GSC) digit recognizer desribed in [8]. The GSC is among the best digit recognizers described in the literature. The method described in this paper successfully reduced its error rate from 2.85% to 1.96%, i.e., by 0.89%, which is more than 30% of the initial error. We have tested our method on other available classifiers and have obtained similar results.