We present results of computer experiments that indicate that several RNAs for which the native state (minimum free energy secondary structure) is functionally important (type III hammerhead ribozymes, signal recognition particle RNAs, U2 small nucleolar spliceosomal RNAs, certain riboswitches, etc.) all have lower folding energy than random RNAs of the same length and dinucleotide frequency. Additionally, we find that whole mRNA as well as 5'-UTR, 3'-UTR, and cds regions of mRNA have folding energies comparable to that of random RNA, although there may be a statistically insignificant trace signal in 3'-UTR and cds regions. Various authors have used nucleotide (approximate) pattern matching and the computation of minimum free energy as filters to detect potential RNAs in ESTs and genomes. We introduce a new concept of the asymptotic Z-score and describe a fast, whole-genome scanning algorithm to compute asymptotic minimum free energy Z-scores of moving-window contents. Asymptotic Z-score computations offer another filter, to be used along with nucleotide pattern matching and minimum free energy computations, to detect potential functional RNAs in ESTs and genomic regions.