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Background: Prioritizing investments across health interventions is complicated by the nonlinear relationship between intervention coverage and epidemiological outcomes. It can be difficult for countries to know which interventions to prioritize for greatest epidemiological impact, particularly when budgets are uncertain., Methods: We examined four case studies of HIV epidemics in diverse settings, each with different characteristics. These case studies were based on public data available for Belarus, Peru, Togo, and Myanmar. The Optima HIV model and software package was used to estimate the optimal distribution of resources across interventions associated with a range of budget envelopes. We constructed "investment staircases", a useful tool for understanding investment priorities. These were used to estimate the best attainable cost-effectiveness of the response at each investment level., Findings: We find that when budgets are very limited, the optimal HIV response consists of a smaller number of 'core' interventions. As budgets increase, those core interventions should first be scaled up, and then new interventions introduced. We estimate that the cost-effectiveness of HIV programming decreases as investment levels increase, but that the overall cost-effectiveness remains below GDP per capita., Significance: It is important for HIV programming to respond effectively to the overall level of funding availability. The analytic tools presented here can help to guide program planners understand the most cost-effective HIV responses and plan for an uncertain future.