Mitochondrial DNA (mtDNA) diseases are a group of neuromuscular diseases that often cause suffering and premature death. New mitochondrial replacement techniques (MRTs) may offer women with mtDNA diseases the opportunity to have healthy offspring to whom they are genetically related. MRTs will likely be ready to license for clinical use in the near future and a discussion of the ethics of the clinical introduction of MRTs is needed. This paper begins by evaluating three concerns about the safety of MRTs for clinical use on humans: (1) Is it ethical to use MRTs if safe alternatives exist? (2) Would persons with three genetic contributors be at risk of suffering? and (3) Can society trust that MRTs will be made available for humans only once adequate safety testing has taken place, and that MRTs will only be licensed for clinical use in a way that minimises risks? It is then argued that the ethics debate about MRTs should be reoriented towards recommending ways to reduce the possible risks of MRT use on humans. Two recommendations are made: (1) licensed clinical access to MRTs should only be granted to prospective parents if they intend to tell their children about their MRT conception by adulthood; and (2) sex selection should be used in conjunction with the clinical use of MRTs, in order to reduce transgenerational health risks.