In this paper, an adaptive scheme for amplify-and-forward relaying networks is proposed, which selects a certain transmission mode for each communication process. Depending on the instantaneous channel conditions, one of the following modes is selected: direct transmission with no cooperation, cooperative transmission with half-duplex relaying and maximal-ratio combining at the destination, or cooperative transmission with full-duplex relaying and maximal-ratio combining at the destination. A three-node network is considered, containing a single-antenna source, a two-antenna relay that is able to implement full-duplex communication, and a single-antenna destination. Energy normalization per block is assumed, so that in those modes using cooperation, the system’s transmission power is shared between source and relay. The performance analysis is provided in terms of outage probability and energy efficiency. We derive a tight approximate expression in closed form for the outage probability and an approximate expression in integral form for the mean energy consumption. The results show that our scheme outperforms all of transmission modes separately in terms of outage probability, while being more energy efficient than the cooperative transmission modes. In addition, the asymptotic analysis proves that the proposed scheme achieves full diversity order equal to 2, thus outperforming those schemes with direct transmission or full-duplex cooperation only.