We have investigated the compositional distributions of third codon positions of genes from the 16 prokaryotes and seven eukaryotes for which the largest numbers of coding sequences are available in data banks. In prokaryotes, both narrow and broad distributions were found. In eukaryotes, distributions were very broad (except for Saccharomyces cerevisiae) and remarkably different for different genomes. In low-GC genomes, third codon positions were lower in GC than first + second codon positions and trailed towards high GC; the opposite situation was found for high-GC genomes. In all genomes, first codon positions were higher in GC than second codon positions. We then investigated the compositional correlations between third and first + second codon positions in prokaryotic genomes (the 16 mentioned above plus 87 additional ones) and in genome compartments of eukaryotes. A general, common relationship was found, which also holds within the same (heterogeneous) genomes. This universal correlation is due to the fact that the relative effects of compositional constraints on different codon positions are the same, on the average, whatever the genome under consideration.