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Pairwise sequence covariations are a signal of conserved RNA secondary structure. We describe a method for distinguishing when lack of covariation signal can be taken as evidence against a conserved RNA structure, as opposed to when a sequence alignment merely has insufficient variation to detect covariations. We find that alignments for several long noncoding RNAs previously shown to lack covariation support do have adequate covariation detection power, providing additional evidence against their proposed conserved structures.