We have developed a new method for estimating the abundance of any modular (piecewise) RNA motif within a longer random region. We have used this method to estimate the size of the active motifs available to modern SELEX experiments (picomoles of unique sequences) and to a plausible RNA World (zeptomoles of unique sequences: 1 zmole = 602 sequences). Unexpectedly, activities such as specific isoleucine binding are almost certainly present in zeptomoles of molecules, and even ribozymes such as self-cleavage motifs may appear (depending on assumptions about the minimal structures). The number of specified nucleotides is not the only important determinant of a motif's rarity: The number of modules into which it is divided, and the details of this division, are also crucial. We propose three maxims for easily isolated motifs: the Maxim of Minimization, the Maxim of Multiplicity, and the Maxim of the Median. These maxims together state that selected motifs should be small and composed of as many separate, equally sized modules as possible. For evenly divided motifs with four modules, the largest accessible activity in picomole scale (1-1000 pmole) pools of length 100 is about 34 nucleotides; while for zeptomole scale (1-1000 zmole) pools it is about 20 specific nucleotides (50% probability of occurrence). This latter figure includes some ribozymes and aptamers. Consequently, an RNA metabolism apparently could have begun with only zeptomoles of RNA molecules.