The nuclear genomes of multicellular animals and plants contain large amounts of noncoding DNA, the disadvantages of which can be too weak to be effectively countered by selection in lineages with reduced effective population sizes. In contrast, the organelle genomes of these two lineages evolved to opposite ends of the spectrum of genomic complexity, despite similar effective population sizes. This pattern and other puzzling aspects of organelle evolution appear to be consequences of differences in organelle mutation rates. These observations provide support for the hypothesis that the fundamental features of genome evolution are largely defined by the relative power of two nonadaptive forces: random genetic drift and mutation pressure.