An important question in biology is why the genetic alphabet is made of just two base pairs (G.C and A.T). This is particularly interesting because of the recent demonstration [Piccirilli, J. A., Krauch, T., Moroney, S. E. & Benner, S. A. (1990) Nature (London) 343, 33-37] that the alphabet can in principle be larger. It is possible to explain the size of the present genetic alphabet as a frozen character state that was an evolutionary optimum in an RNA world when nucleic acids functioned both for storing genetic information and for expressing information as enzymatically active RNA molecules--i.e., ribozymes. A previous model [Szathmáry, E. (1991) Proc. R. Soc. London Ser. B 245, 91-99] has described the principle of this approach. The present paper confirms and extends these results by showing explicitly the ways in which copying fidelity and metabolic efficiency change with the size of the genetic alphabet.