Achieving energy self-sufficiency is a major challenge for remote areas, especially islands. Various technologies have recently been developed to exploit renewable resources in such areas in order to reduce dependency on fossil fuels. This work focuses on the situation of Easter Island, a representative example of a remote area, and explores the pros and cons of three fully renewable energy mixes used to meet local requirements. This investigation reveals that, while a classic photovoltaic/battery combination allows demands to be met, the installations need to be oversized, leading to a 73% loss in the total energy produced. By adding alternative energy production sources such as wind turbines and pyrolysis, as well as alternative storage systems such as hydrogen-based storage, the energy loss is divided by a factor of 5. This more diverse energy mix enables a reasonable electricity price of 0.18 €/kWh, which is comparable to the current local prices. This work reinforces the importance of complementary energy production and storage systems to efficiently meet the energy requirements of islands.