In this paper, we have studied the energy efficiency of cooperative networks operating in either the fixed Amplify-and-Forward (AF) or the selective Decode-and-Forward (DF) mode. We consider the optimization of the M-ary quadrature amplitude modulation (MQAM) constellation size to minimize the bit energy consumption under given bit error rate (BER) constraints. In the computation of the energy expenditure, the circuit, transmission, and retransmission energies are taken into account. The link reliabilities and retransmission probabilities are determined through the outage probabilities under the Rayleigh fading assumption. Several interesting observations with practical implications are made. For instance, it is seen that while large constellations are preferred at small transmission distances, constellation size should be decreased as the distance increases. Moreover, the cooperative gain is computed to compare direct transmission and cooperative transmission.