Pathogens are a significant driver of biodiversity loss. We examine two wildlife disease management strategies that have seen growing use, sometimes in combination: (i) trapping-and-culling infectious animals (disease control), and (ii) trapping-and-translocating healthy animals to a reserve, with possible future reintroduction. A reserve can improve conservation when there is no disease. But, when infection exists, we show investing in the reserve may counteract disease control. We find jointly pursuing both strategies is sub-optimal when the reserve is costly to maintain. Numerically, we examine management of Devil Facial Tumor Disease, which has generated extinction risks for Tasmanian Devils. Disease control (though not eradication) is generally part of an optimal strategy, although a reserve is also optimal if it can be maintained costlessly. This implies preserving the original population by addressing in situ conservation risks, rather than translocating animals to a reserve and giving up on the original population, is generally the first-best.