Resource constraints in ad hoc wireless networks require that they are energy efficient during both transmission and rate adaptation. In this paper, we propose a novel energy-efficient rate adaptation protocol that selects modulation schemes online to maximize throughput based on channel state while saving energy. This protocol uses the distributed power control (DPC) algorithm (M. Zawodniok et al., 2004) to accurately determine the necessary transmission power and to reduce the energy consumption. Additionally, the transmission rate is altered using energy efficiency as a constraint to meet the required throughput, which is estimated with queue fill ratio. Moreover, back-off scheme is incorporated to prevent energy wastage and to avoid retransmissions in the event of congestion. The back-off scheme employs backpressure mechanism to emulate congestion control. Consequently, the nodes will conserve energy when the traffic is low, offer higher throughput when needed and save energy during congestion by limiting transmission.