Background: Efforts to develop an HIV "cure" (i.e., an intervention leading to durable ART-free remission or eradication of HIV infection) have become better resourced and coordinated in recent years. Given, however, the availability of other interventions for prevention and treatment of HIV disease, it is unclear whether, to what extent, and under which circumstances a curative intervention would have an impact in ending the AIDS epidemic and which characteristics of its implementation would be most important. We designed a range of analyses to investigate these unknowns. Methods: We used a deterministic, compartmental model of HIV infection in South Africa to estimate the impact of a curative intervention. We first examined how its impact would be affected by the state of the epidemic at the time that it is introduced, by the timing and pace of scale-up, and by various targeting strategies. We then investigated the impact of a curative intervention relative to its ability to maintain viral suppression. Findings: To the extent that other interventions have failed to control the epidemic, i.e., if incidence and AIDS deaths remain high, a curative intervention would result in a larger reduction in incidence. Earlier and faster scale-up allows for greater impact. We also found that a curative intervention would more efficiently reduce transmission if it is prioritised to those not able to obtain or remain on ART and to those aged 15-25 rather than older persons. On the other hand, an intervention that does not maintain viral suppression if the individual is exposed to re-infection could lead to an increase in HIV incidence. Conclusions: Our findings suggest that a curative intervention for HIV would have the greatest impact if the epidemic is not under control by 2030, particularly if the intervention is targeted to those who are more likely to transmit virus, and if it maintained durable viral suppression, even upon exposure to re-infection. These considerations underscore the need to carefully consider the "target product profiles" for an HIV cure in the context of how and where it would be used, and suggest that such profiles may require revision as the epidemic evolves in the coming years.