The proliferation of wireless networks based on IEEE 802.11 has resulted in a heterogenous set of devices using a variety of applications to compete for the desired service performance. Most notably, the class of highly mobile and energy constrained devices is showing high growth rates. Yet, fairness of resource allocation is still only considered in terms of achievable throughput and without considering energy efficiency. In this paper we first show that performing an energy efficient and fair resource allocation in current IEEE 802.11 WLANs is challenging, given the diversity of power consumption figures among mobile devices. We then propose a criterion to objectively balance between the most energy-efficient configuration (where all resources are given to one station) and the throughput-fair allocation (where the power consumption is not considered). We derive a closed-form expression for the optimal configuration of 802.11 with respect to this criterion. Our analysis is validated through simulations, showing that our approach betters the prevalent allocation schemes discussed in literature in terms of energy efficiency, while maintaining the notion of fairness among devices. Experimental results obtained in a real-world testbed confirm the main results derived from our analysis and simulations.