Mitochondrial replacement therapy (MRT) is a human reproductive technology by which the mitochondria of a recipient's eggs are effectively replaced by those of a donor, potentially eliminating harmful mitochondrial mutations carried by the recipient. However, concerns have been raised that MRT may lead to problems due to incompatibilities between the nuclear genome of the recipient and mitochondrial genome of the donor. Whether this is likely to be a problem is investigated using 226 estimates, taken from the literature, of the effect of replacing the "native" by a "foreign" mitochondrial DNA (mtDNA) from the same species in a variety of animals. In approximately half of the cases (45%), strains with the foreign mtDNA have higher fitness than those with the native mtDNA, and on average the native strains are only 3% fitter. Based on these results it is argued that incompatibilities between the mitochondrial and nuclear genomes are not likely to be a problem for MRT.