Mitochondrial medicine is one of the few areas of genetic disease where germ-line transfer is being actively pursued as a treatment option. All of the germ-line transfer methods currently under development involve some carry-over of the maternal mitochondrial DNA (mtDNA) heteroplasmy, potentially delivering the pathogenic mutation to the offspring. Rapid changes in mtDNA heteroplasmy have been observed within a single generation, and so any 'leakage' of mutant mtDNA could lead to mtDNA disease in future generations, compromising the reproductive health of the first generation, and leading to repeated interventions in subsequent generations. To determine whether this is a real concern, we developed a model of mtDNA heteroplasmy inheritance by studying 87 mother-child pairs, and predicted the likely outcome of different levels of 'mutant mtDNA leakage' on subsequent maternal generations. This showed that, for a clinical threshold of 60%, reducing the proportion of mutant mtDNA to <5% dramatically reduces the chance of disease recurrence in subsequent generations, but transmitting >5% mutant mtDNA was associated with a significant chance of disease recurrence. Mutations with a lower clinical threshold were associated with a higher risk of recurrence. Our findings provide reassurance that, at least from an mtDNA perspective, methods currently under development have the potential to effectively eradicate pathogenic mtDNA mutations from subsequent generations.