In ancient genes whose products have known 3-dimensional structures, an excess of phase zero introns (those that lie between the codons) appear in the boundaries of modules, compact regions of the polypeptide chain. These excesses are highly significant and could support the hypothesis that ancient genes were assembled by exon shuffling involving compact modules. (Phase one and two introns, and many phase zero introns, appear to arise later.) However, as more genes, with larger numbers of homologs and intron positions, were examined, the effects became smaller, dropping from a 40% excess to an 8% excess as the number of intron positions increased from 570 to 3,328, even though the statistical significance remained strong. An interpretation of this behavior is that novel inserted positions appearing in homologs washed out the signal from a finite number of ancient positions. Here we show that this is likely to be the case. Analyses of intron positions restricted to those in genes for which relatively few intron positions from homologs are known, or to those in genes with a small number of known homologous gene structures, show a significant correlation of phase zero intron positions with the module structure, which weakens as the density of attributed intron positions or the number of homologs increases. These effects do not appear for phase one and phase two introns. This finding matches the expectation of the mixed model of intron origin, in which a fraction of phase zero introns are left from the assembly of the first genes, while other introns have been added in the course of evolution.