Lateral gene transfers are frequent among prokaryotes, although their detection remains difficult. If all genes are equally affected, this questions the very existence of an organismal phylogeny. The complexity hypothesis postulates the existence of a core of genes (those involved in numerous interactions) that are unaffected by transfers. To test the hypothesis, we studied all the proteins involved in translation from 45 eubacterial taxa, and developed a new phylogenetic method to detect transfers. Few of the genes studied show evidence for transfer. The phylogeny based on the genes devoid of transfer is very consistent with the ribosomal RNA tree, suggesting that an eubacterial phylogeny does exist.