Most COVID-19 vaccines require two doses, and current vaccine prioritization guidelines for COVID-19 vaccines assume full-dose vaccine deployment. However in the context of limited vaccine supply and an expanding pandemic, policymakers are considering single-dose vaccination as an alternative strategy. Using a mathematical model combined with optimization algorithms, we determined the optimal allocation with one and two doses of vaccine to minimize five metrics of disease burden under various degrees of viral transmission. Under low transmission, we show that the optimal allocation of vaccine critically depends on the level of single-dose efficacy (SDE). If the SDE is high, single-dose vaccination is optimal, preventing up to 36% more deaths than a strategy prioritizing full-dose vaccination for older adults first. With low or moderate SDE, mixed vaccination campaigns with coverage of all older adults with one dose are optimal. However, with modest or high transmission, vaccinating older adults first with two doses is best, preventing up to 41% more deaths than a single-dose vaccination given across all populations. Further, we show that maintaining social distancing interventions and speedy deployment are key for effective vaccination campaigns. Our work suggests that it is imperative to determine the efficacy and durability of single-dose vaccines, as mixed or single-dose vaccination campaigns may have the potential to contain the pandemic much more quickly.