Motivation: Recently, we described a Maximum Weighted Matching (MWM) method for RNA structure prediction. The MWM method is capable of detecting pseudoknots and other tertiary base-pairing interactions in a computationally efficient manner. Here we report on the results of our efforts to improve the MWM method's predictive accuracy and show how the method can be extended to detect base interactions formerly inaccessible to automated RNA modeling techniques. Results: Improved performance in MWM structure prediction was achieved in two ways. First, new ways of calculating base pair likelihoods have been developed. These allow experimental data and combined statistical and thermodynamic information to be used by the program. Second accuracy was improved by developing techniques for filtering out spurious base pairs predicted by the MWM program. We also demonstrate here a means by which the MWM folding method may be used to detect the presence of base triples in RNAs. Availability: http://www.cshl.org/mzhanglab/tabaska/jax-page.html. Contact: tabaska@@@cshl.org.