In this paper, we exploit the benefits of combining the diversity gains that arise from cooperation, multiple propagation paths, and opportunistic relaying (OR) of multiple users. Our goal is to improve the energy efficiency of the amplify-and-forward (AF) single-relay-assisted single-carrier frequency-division multiple-access (SC-FDMA) uplink, where the single relay considered may support a single user or may be shared by multiple users who communicate over dispersive channels subject to large-scale fading. Based on the proposed amalgam of single-tap frequency-domain equalization (FDE) and a diversity-combining-aided receiver that relies on the minimum mean-square error (MMSE) criterion, three different relay selection schemes designed for either single-user or multiuser relaying scenarios are investigated, when combined with source/relay power sharing, which employ imperfect power control. Our results demonstrate that, at a bit error ratio (BER) of 10(-4), the proposed receiver can save 2 dB power by achieving a higher cooperative diversity gain than the conventional receiver. Moreover, a beneficial energy efficiency improvement may be achieved when the cooperative regime operates at E-b/N-0 < 0. Most importantly, when the shadowing variance is increased from 4 dB to 8 dB, the energy consumption gain gleaned from our multiuser and multiaccess relay selection schemes may increase to 4 similar to 9, compared with the direct transmission in the absence of shadowing at E-b/N-0 = -10 dB.