Non-coding RNAs (ncRNAs) are functional RNA molecules that do not code for proteins. Covariance Models (CMs) are a useful statistical tool to find new members of an ncRNA gene family in a large genome database, using both sequence and, importantly, RNA secondary structure information. Unfortunately, CM searches are extremely slow. Previously, we created rigorous filters, which provably sacrifice none of a CMs accuracy, while making searches significantly faster for virtually all ncRNA families. However, these rigorous filters make searches slower than heuristics could be.