The problem of choosing the correct number of clusters is as old as cluster analysis itself. A number of authors have suggested various indexes to facilitate this crucial decision. One of the most extensive comparative studies of indexes was conducted by Milligan & Cooper (1985). The present piece of work pursues the same goal under different conditions. In contrast to Milligan and Cooper's work, the emphasis here is on high-dimensional empirical binary data. Binary artificial data sets are constructed to reflect features typically encountered in real-world situations in the field of marketing research. The simulation includes 162 binary data sets that are clusters by two different algorithms and lead to recommendations on the number of clusters for each index under consideration. Index results are evaluated and their performance is compared and analysed.