Traditional approaches to combining classifiers attempt to improve classification accuracy at the cost of increased processing. They may be viewed as providing an accuracy-speed trade-off: higher accuracy for lower speed. In this paper we present a novel approach to combining multiple classifiers to solve the inverse problem of significantly improving classification speeds at the cost of slightly reduced classification accuracy. We propose a cascade architecture for combining classifiers and cast the process of building such a cascade as a search and optimization problem. We present two algorithms based on steepest-descent and dynamic programming for producing approximate solutions fast. We also present a simulated annealing algorithm and a depth-first-search algorithm for finding optimal solutions. Results on handwritten optical character recognition indicate that a) a speedup of 4-9 times is possible with no increase in error and b) speedups of up to 15 times are possible when twice ...