It remains controversial why mitochondria and chloroplasts retain the genes encoding a small subset of their constituent proteins, despite the transfer of so many other genes to the nucleus. Two candidate obstacles to gene transfer, suggested long ago, are that the genetic code of some mitochondrial genomes differs from the standard nuclear code, such that a transferred gene would encode an incorrect amino acid sequence, and that the proteins most frequently encoded in mitochondria are generally very hydrophobic, which may impede their import after synthesis in the cytosol. More recently it has been suggested that both these interpretations suffer from serious "false positives" and "false negatives": genes that they predict should be readily transferred but which have never (or seldom) been, and genes whose transfer has occurred often or early, even though this is predicted to be very difficult. Here I consider the full known range of ostensibly problematic such genes, with particular reference to the sequences of events that could have led to their present location. I show that this detailed analysis of these cases reveals that they are in fact wholly consistent with the hypothesis that code disparity and hydrophobicity are much more powerful barriers to functional gene transfer than any other. The popularity of the contrary view has led to the search for other barriers that might retain genes in organelles even more powerfully than code disparity or hydrophobicity; one proposal, concerning the role of proteins in redox processes, has received widespread support. I conclude that this abandonment of the original explanations for the retention of organellar genomes has been premature. Several other, relatively minor, obstacles to gene transfer certainly exist, contributing to the retention of relatively many organellar genes in most lineages compared to animal mtDNA, but there is no evidence for obstacles as severe as code disparity or hydrophobicity. One corollary of this conclusion is that there is currently no reason to suppose that engineering nuclear versions of the remaining mammalian mitochondrial genes, a feat that may have widespread biomedical relevance, should require anything other than sequence alterations obviating code disparity and causing modest reductions in hydrophobicity without loss of enzymatic function.