Covariation induced by compensatory base substitutions in RNA alignments is a great way to deduce conserved RNA structure, in principle. In practice, success depends on many factors, importantly the quality and depth of the alignment and the choice of covariation statistic. Measuring covariation between pairs of aligned positions is easy. However, using covariation to infer evolutionarily conserved RNA structure is complicated by other extraneous sources of covariation such as that resulting from homologous sequences having evolved from a common ancestor. In order to provide evidence of evolutionarily conserved RNA structure, a method to distinguish covariation due to sources other than RNA structure is necessary. Moreover, there are several sorts of artifactually generated covariation signals that can further confound the analysis. Additionally, some covariation signal is difficult to detect due to incomplete comparative data. Here, we investigate and critically discuss the practice of inferring conserved RNA structure by comparative sequence analysis. We provide new methods on how to approach and decide which of the numerous long non-coding RNAs (lncRNAs) have biologically relevant structures.