A number of important applications require the clustering of binary data sets. Traditional nonhierarchical cluster analysis techniques, such as the popular K-means algorithm, can often be successfully applied to these data sets. However, the presence of masking variables in a data set can impede the ability of the K-means algorithm to recover the true cluster structure. The author presents a heuristic procedure that selects an appropriate subset from among the set of all candidate clustering variables. Specifically, this procedure attempts to select only those variables that contribute to the definition of true cluster structure while eliminating variables that can hide (or mask) that true structure. Experimental testing of the proposed variable-selection procedure reveals that it is extremely successful at accomplishing this goal.