While sexually-reproducing organisms each contribute nuclear DNA to their offspring, mitochondrial DNA is generally transmitted by a single parent. This is true for species with sexes, where mitochondria are typically inherited from the female, and in single-celled species that lack defined sexes and instead have mating types. The current explanation for uniparental inheritance is the genomic conflict theory, which hypothesises that uniparental inheritance has evolved to mitigate conflict between the mitochondrial and nuclear genomes. If mitochondria from both parents were allowed to mix, it could select for fast replicating, but energetically inefficient, 'selfish' mitochondria, which could spread and severely lower cell fitness. A recent empirical study in mice has indicated that the mixing of different, but normal, mitochondria lineages (heteroplasmy) could be sufficient to cause organism dysfunction. Could it be that cells avoid mixing mitochondrial haplotypes simply because it is costly? Here, I present a mathematical model that examines whether costs from mixing mitochondrial haplotypes could have led to the evolution of uniparental inheritance in an ancestrally-biparental population.