Frank Wright [Gene 87 (1990) 23] derived a formula for calculation of a quantity termed the 'effective number of codons' ((N) over capc) based on codon homozygosities. This quantity is a number between 20 and 61 and tells to what degree the codon usage in a gene is biased. i.e.. it approaches 20 codons for the extremely biased genes, and approaches 61 for the genes where all possible codons are used with no preference. Among the different measures of codon bias (N) over capc is considered the most useful and has found widespread use in papers dealing with codon usage phenomena. In this paper, the mathematical behaviours of codon homozygosities and (N) over capc are evaluated. using Escherichia coli as the model organism. The results indicate that the classical formula for calculation of (N) over capc Could appropriately be substituted under circumstances, where there is bias discrepancy, i.e., when one amino acid (or more) within a degeneracy group is associated with strong codon bias while at the same time others in the same degeneracy group have little bias. An alternative estimator termed (N) over capc*, is proposed and tested against (N) over capc, and performs better when there is such bias discrepancy. (C) 2004 Elsevier Inc. All rights reserved.