Genetic rescue can reduce the extinction risk of inbred populations, but it has the poorly understood risk of ‘genetic swamping’—the replacement of the distinctive variation of the target population. We applied population viability analysis (PVA) to identify translocation rates into the inbred lowland population of Leadbeater’s possum from an outbred highland population that would alleviate inbreeding depression and rapidly reach a target population size (N) while maximising the retention of locally unique neutral genetic variation. Using genomic kinship coefficients to model inbreeding in Vortex, we simulated genetic rescue scenarios that included gene pool mixing with genetically diverse highland possums and increased the N from 35 to 110 within ten years. The PVA predicted that the last remaining population of lowland Leadbeater’s possum will be extinct within 23 years without genetic rescue, and that the carrying capacity at its current range is insufficient to enable recovery, even with genetic rescue. Supplementation rates that rapidly increased population size resulted in higher retention (as opposed to complete loss) of local alleles through alleviation of genetic drift but reduced the frequency of locally unique alleles. Ongoing gene flow and a higher N will facilitate natural selection. Accordingly, we recommend founding a new population of lowland possums in a high-quality habitat, where population growth and natural gene exchange with highland populations are possible. We also recommend ensuring gene flow into the population through natural dispersal and/or frequent translocations of highland individuals. Genetic rescue should be implemented within an adaptive management framework, with post-translocation monitoring data incorporated into the models to make updated predictions.