This paper reports the existence of a significant negative correlation between GC12 and GC3 in the recently sequenced genome of Leishmania major. This result contradicts the previous evidence that the compositional correlations between codon positions are universal. Moreover, it challenges the interpretation of the GC12 vs. GC3 linear regression slope as the relative neutrality of GC12, within the framework of the directional mutation pressure theory [Sueoka, N., 1988. Directional mutational pressure and neutral molecular evolution. P Natl Acad Sci USA 85, 2653–2657.].The analysis of the codon usage pattern for L. major shows that codon choice is most likely influenced by both mutation pressure and translational selection. Dinucleotide frequencies were also analysed; our results do not support the existence of an unusual neighbour-dependent mutation bias in this genome.We developed two evolutionary models that could explain the origin of the negative GC12/GC3 correlation. The first model is based on the effect of translational selection on the GC3 the second one is based on a potential mutation bias combined with purifying selection at the amino-acid level. Both models predict a negative GC12/GC3 correlation at the equilibrium. The potential implications of these results for this aspect of the directional mutation pressure theory are discussed. We conclude that the particular case of L. major should lead to a careful reevaluation of several hypotheses of this theory. The origin of the negative GC12/GC3 correlation remains for now an open question.