Energy-efficiency (EE) is a critical metric in many types of wireless networks and is getting increasingly important for new technologies. In this paper, the authors propose an energy-efficient decode-and-forward relaying strategy for two-hop diamond networks where the source-destination communication is established by the help of two relays which have an inter-relay link. The inter-relay link gives the opportunity of correcting the data packet between relays if only one of them decodes the packet that is received from the source correctly. Hence, both relays are able to send the data packet to the destination with distributed Alamouti coding which provides multipath diversity. In addition, they introduce optimum data rate adaptation for each link separately to maximise EE for the considered network. By exploiting diversity and optimum rate adaptation, it is possible to transmit at higher rates with reasonable outage probability which has critical effects on EE and throughput. They show via computer simulations that the proposed technique is substantially more energy-efficient and has a better throughput than the successive relaying technique given in the literature; moreover, more robust to the changes in system conditions, i.e. relay location and transmission power level.