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Prediction of common secondary structure across multiple RNA sequences is known to significantly increase accuracy in comparison with single-sequence based prediction methods. However, the computational requirements for joint prediction can often be daunting in comparison to single-sequence prediction. As a result, heuristic simplifications are often necessary for this joint estimation problem in order to perform computations on current hardware in reasonable times. In this paper, principled heuristics are presented for the purpose of computation reduction based on probabilistic methods. The methods presented eliminate the computations over extremely improbable alignments and structures, thereby reducing computation with little or no degradation in accuracy. Experimental results over databases of RNA families with known secondary structure validate our methods, demonstrating over a two-fold computational speed up in tests over the 5 S rRNA family, without any compromise in accuracy.