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The most accurate methods for RNA secondary structure prediction simultaneously predict the common structure and alignment among multiple homologs. In addition to dynamic programming, practical algorithms utilize heuristics to restrict the search space and further reduce time and memory requirements. This work is directed toward improving these heuristics in order to reduce computation without a compromise in accuracy. In this paper, a new, principled method for restricting the alignment search space in Dynalign  is introduced. Our results indicate that we are able to improve runtime with little affect on the accuracy of the structure predictions. This work utilizes Dynalign, but this method is also applicable to other structure prediction programs.