Recently, there has been much interest in exploring the universe of non-protein coding RNA molecules that operate in the cell. We suggested an approach using a simple two-dimensional representation of RNA molecules that can identify common structural features of RNA molecules. Here, we address a common situation in which there is a large and diverse population of candidate molecules, and the task is to identify a small subset (or subsets) of RNA molecules that share a common structure. With certain constraints, our algorithm enumerates all possible sets of RNA molecules that have a common structure by first grouping together all molecules that have a single common structural feature and, using an iterative approach, search for subsets that share additional structural motifs. In a computational experiment, we were able to detect members of three small classes of RNA molecules, each containing several dozen members that were mixed in a population of 2778 non-coding sequences common to two trypanosome species.