A procedure is given which substantially reduces the processing time needed to perform maximum likelihood classification on large data sets. The given method uses a set of fixed thresholds which, if exceeded by one probability density function, makes it unnecessary to evaluate a competing density function. Proofs are given of the existence and optimality of these thresholds for the class of continuous, unimodal, and quasi-concave density functions (which includes the multivariate normal), and a method for computing the thresholds is provided for the specifilc case of multivariate normal densities. An example with remote sensing data consisting of some 20 000 observations of four-dimensional data from nine ground-cover classes shows that by using thresholds, one could cut the processing time almost in half.