The interplay between the internet of things, big data, cloud computing and mobility has brought up a number of challenges. One of them is the reliance of handheld wireless communication devices, e.g. smartphones, on limited battery power. In this paper we contribute to efforts that address this challenge. We investigate the energy efficiency of MAC layer fragmentation scheme. Despite the usefulness of fragmentation in improving transmission reliability in poor quality wireless channels, it comes with overhead costs that lead to its energy inefficiency. When a fragment transmission fails (due to collisions or channel induced errors), extra contentions are executed and hence extra overheads are incurred. We propose a novel fragmentation scheme called backoff-free fragment retransmission (BFFR). BFFR addresses classical fragmentation overheads. It aims at improving classical fragmentation energy efficiency without adversely affecting its throughput. We implement BFFR in NS3 and performance evaluation showed that BFFR outperforms classical fragmentation scheme in both throughput and energy efficiency. Further performance evaluation results indicate that our scheme maintained MAC delay performance of distributed coordination function at a small cost of medium access fairness in small sized wireless local area networks (WLANs). BFFR can be employed in legacy IEEE 802.11 networks to enhance their energy efficiency and throughput in poor quality wireless channels.