BACKGROUND: RNA secondary structure prediction methods based on probabilistic modeling can be developed using stochastic context-free grammars (SCFGs). Such methods can readily combine different sources of information that can be expressed probabilistically, such as an evolutionary model of comparative RNA sequence analysis and a biophysical model of structure plausibility. However, the number of free parameters in an integrated model for consensus RNA structure prediction can become untenable if the underlying SCFG design is too complex. Thus a key question is, what small, simple SCFG designs perform best for RNA secondary structure prediction? RESULTS: Nine different small SCFGs were implemented to explore the tradeoffs between model complexity and prediction accuracy. Each model was tested for single sequence structure prediction accuracy on a benchmark set of RNA secondary structures. CONCLUSIONS: Four SCFG designs had prediction accuracies near the performance of current energy minimization programs. One of these designs, introduced by Knudsen and Hein in their PFOLD algorithm, has only 21 free parameters and is significantly simpler than the others.