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It is commonly assumed that the energy consumption of wireless communications is minimized when low-order modulations such as BPSK are used. Nevertheless, the literature provides some evidence that low-order modulations are suboptimal for short transmission distances. No complete analysis on how the modulation size and transmission power must be chosen in order to achieve energy-efficient communications over fading channels has been reported so far. In this paper we provide this analysis by presenting a model that determines the energy consumed per payload bit transferred without error over fading channels of various statistics. We find that each modulation scheme has a single optimal signal-to-noise ratio (SNR) at which the energy consumption is minimized. The optimal SNR and the minimal energy consumption are larger for channels with less favorable error statistics. We also find that, if each modulations is operated at its optimal SNR, BPSK and QPSK are the optimal choices for long transmission distances, but as the transmission distance shortens the optimal modulation size grows to 16-QAM and even to 64-QAM. This result leads to showing that for short-range communications the lifetime of a typical low-power transceiver can be up to 500% longer by selecting the optimal constellation instead of BPSK.