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The genetic code is examined in a new and systematic fashion: we consider the code as mapping of one finite set (the 64 codons) to another (the 20 amino acids). Given a class of mappings simpler than the actual code, we ask which mappings best approximate it. This leads to an analysis of the effects of ambiguities (codon degeneracy) in one or two positions. With the 0-1 metric (counting the amino acids as equal or not equal), the codon third base degeneracy is apparent, but the first and second positions are indistinguishable; with the integrated amino acid “distance” metric compiled by Sneath (J. Theoret. Biol. 12 (1966), 157-195), the analysis ranks the information content of the three codon positions as follows: 2nd> 1st> 3rd. We discuss possible further applications of this approach to patterns in the genetic code and other codes. 0 1988 Academic Press. Inc. 1