This paper presents a distributed mechanism for improving the overall energy efficiency of a wireless network where users can control their uplink transmit power targeted to the multiple access points in the network. This mechanism lets the network achieve a trade-off between energy efficiency and spectral efficiency through the use of suitably designed utility functions. A user's utility is a function of throughput and average transmission power. Throughput is assumed to be a sigmoidal function of signal-to-interference-plus-noise ratio. Each user, being selfish and rational, acts to maximise its utility in response to signal-to-interference-plus-noise ratio by adjusting its power. The resulting mechanism is a distributed power control scheme that can incline towards energy-efficient or spectrally efficient operating points depending on the choice of utility function. Existence and uniqueness of Nash equilibrium points in this game are shown via convergence of the distributed power iterations. It is shown that, in the best-response strategy, each user selects a single access point. An extension of this result for a multicarrier system is considered, and the corresponding power levels used for various priorities between energy efficiency and spectral efficiency are characterised. Finally, several numerical studies are presented to illustrate the analysis. Copyright (c) 2012 John Wiley & Sons, Ltd.