Energy Sustainability has been addressed through advancing technology efficiency, which may increase the impact of the use of natural resources. However, the increase in efficiency makes services cheaper, which causes a rebound effect, direct or indirect, on energy consumption and materials. Moreover, the popular concept of recycling seems insufficient to reduce the use of critical raw materials to provide energy services. From the perspective of the Earth’s limited resources, the sustainability problem needs a design approach to tackle the rebound effect from efficiency. This work aims to create a theoretical holistic review regarding energy use linked to technology efficiency, to understand how rebound effects may be prevented. In this work, the Axiomatic Design (AD) theory creates the framework that defines the Energy Sustainability functions and identifies the couplings that create the rebounds. According to AD, cycles occur on coupled designs, classified as poor designs. Decoupling the design clarifies two possible and complementary policies to achieve sustainability goals regarding the use of resources. The first is the circular economy, with constraints on energy and raw materials. The second is the massive use of local renewable energies. Plausible solutions come from mandating efficiency and taxation, dematerializing the economy, and reducing, reusing, remanufacturing, and recycling materials from products and systems. These solutions impact economic, environmental, and societal behaviors. The novelty of this approach is the definition of a system model for Energy Sustainability in the frame of AD, while tackling the rebound effect from technological efficiency.