Motivation: 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 CM's accuracy, while making searches significantly faster for virtually all ncRNA families. However, these rigorous filters make searches slower than heuristics could be. Results: In this paper we introduce profile HMM-based heuristic filters. We show that their accuracy is usually superior to heuristics based on BLAST. Moreover, we compared our heuristics with those used in tRNAscan-SE, whose heuristics incorporate a significant amount of work specific to tRNAs, where our heuristics are generic to any ncRNA. Performance was roughly comparable, so we expect that our heuristics provide a high-quality solution that-unlike family-specific solutions-can scale to hundreds of ncRNA families.