Much effort has been devoted to development of methods to reduce hyperspectral image dimensionality by locating and retaining data relevant for image interpretation while discarding that which is irrelevant. Irrelevance can result from an absence of information that could contribute to the classification, or from the presence of information that could contribute to the classification but is redundant with other information already selected for inclusion in the classification process. We describe a new supervised method that uses mutual information to incrementally determine the most relevant combination of available bands and/or derived pseudo bands to differentiate a specified set of classes. We refer to this as relevance spectroscopy. The method identifies a specific optimum band combination and provides estimates of classification accuracy for data interpretation using a complementary, also information theoretic, classification procedure. When modest numbers of classes are involved the number of relevant bands to achieve good classification accuracy is typically three or fewer. Time required to determine the optimum band combination is of the order of a minute on a personal computer. Automated interpretation of intermediate images derived from the optimum band set can often keep pace with data acquisition speeds.