We have examined the utility of a graph-theoretic algorithm for building comparative RNA models. The method uses a maximum weighted matching algorithm to find the optimal set of base-pairs given the mutual information for all pairs of alignment positions. In all cases examined, the technique generated models similar to those based on conventional comparative analysis. Any set of pairwise interactions can be suggested including pseudoknots. Here we describe the details of the method and demonstrate its implementation on tRNA where many secondary and tertiary base-pairs are accurately predicted. We also examine the usefulness of the method for the identification of shared structural features in families of RNAs isolated by artificial selection methods such as SELEX.