Combination of Multiple Classifiers (CMC) has recently drawn attention as a method of improving classification accuracy. This paper presents a method for combining classifiers that uses estimates of each individual classifier's local accuracy in small regions of feature space surrounding an unknown test sample. Only the output of the most locally accurate classifier is considered. We address issues of 1) optimization of individual classifiers, and 2) the effect of varying the sensitivity of the individual classifiers on the CMC algorithm. Our algorithm performs better on data from a real problem in mammogram image analysis than do other recently proposed CMC techniques.