Tropical cloud fractions from combined CALIPSO and CloudSat observations are classified based on a K-means cluster analysis. These satellite instruments together retrieve detailed vertical structure of clouds, allowing for an objective decomposition of tropical clouds into distinct regimes. The identified cloud regimes are overall robust except that an increasing number of redundant high-cloud clusters are produced as the specified number of clusters is increased. This redundancy arises because geometrically thin clouds with slightly different altitudes can be mathematically distant from one another in the clustering procedure despite their morphological similarity, suggesting that an excessive number of clusters only generate unrealistic subclasses of high clouds. Objective evaluation metrics indicates that the most appropriate number of clusters is four, where the clusters may be labeled as near clear-sky, low cloud, high cloud, and deep convective regimes. A five-cluster classification is also deemed as reasonable, where a fifth regime of congestus clouds joins the other four regimes practically equivalent to the four-cluster solution. This study suggests that determining the optimal clustering solutions requires a careful interpretation from meteorological perspectives beyond a mere statistical assessment of clustering performance.