In this paper we introduce the Energy-Efficient Multiple Access (EE-MA) protocol for wireless networks where nodes participate in a distributed election to gain interference-free access to the wireless channel. By taking advantage of the information used in the distributed elections, nodes can infer if they are not the intended receiver of a transmission and set their radios in sleeping state to save energy. To save even more energy and avoid false positives derived from the nature of the protocol, EE-MA also implements a sleeping scheme where nodes switch to the sleeping state if no message is received during the beginning of a time-slot. We show that the individual channel access plans computed by the proposed distributed algorithm are collision-free at the intended receivers and that intended receivers are always in receiving state. We also present a simulation-based performance analysis that shows that EE-MA outperforms a state of the art election-based channel access protocol in terms of energy efficiency with no cost in terms of network capacity. Simulations also show that EE-MA outperforms 802.11 contention based protocol in terms of goodput and channel access delay.