Piccirilli et al. (Nature, Lond. 343, 33-37 (1990)) have shown experimentally that the replicatable introduction of new base pairs into the genetic alphabet is chemically feasible. The fact that our current genetic alphabet uses only two base pairs can be explained provided that this basic feature of organisms became fixed in an RNA world utilizing ribozymes rather than protein enzymes. The fitness of such riboorganisms is determined by two factors: replication fidelity and overall catalytic efficiency (basic metabolic or growth rate). Replication fidelity is shown to decrease roughly exponentially, and catalytic efficiency is shown to increase with diminishing returns, with the number of letters for a fixed genome length; hence their product, i.e. fitness, gives rise to a set of values with an optimum. Under a wide range of parameter values the optimum rests at two base pairs. The chemical identity of the particular choice in our genetic alphabet can also be rationalized. This optimum is considered frozen, as currently the dominant catalysts are proteins rather than RNAs.