Carrier Sense Multiple Access (CSMA) is widely used as a Medium Access Control (MAC) in wireless networks due to its simplicity and distributed nature. This motivated researchers to find CSMA schemes that achieve throughput optimality. In 2008, it has been shown that a simple CSMA-type algorithm is able to achieve optimality in terms of throughput and has been given the name "adaptive" CSMA. Lately, new technologies emerged where prolonged battery life is crucial such as environment and industrial monitoring. This inspired the foundation of new CSMA based MAC schemes where links are allowed to transition into sleep mode to reduce the power consumption. However, throughput optimality of these schemes was not established. This paper therefore aims to find a new CSMA scheme that combines both throughput optimality and energy efficiency by adapting to the throughput and power consumption needs of each link. This is done by controlling operational parameters such as back-off and sleeping timers with the aim of optimizing a certain objective function. The resulting CSMA scheme is characterized by being asynchronous, completely distributed and being able to adapt to different power consumption profiles required by each link while still ensuring throughput optimality. The performance gain in terms of energy efficiency compared to the conventional adaptive CSMA scheme is demonstrated through computer simulations.