Cooperative-diversity networks have recently been proposed as a way to form virtual antenna arrays without using collocated multiple antennas. Cooperative-diversity networks use the neighbor nodes to assist the source by sending the source information to the destination for achieving spatial diversity. Regular cooperative-diversity networks make an inefficient use of the channel resources because relays forward the source signal to the destination every time regardless of the channel conditions. Incremental relaying cooperative diversity has been proposed to save the channel resources by restricting the relaying process to the bad channel conditions only. Incremental relaying cooperative relaying networks exploit limited feedback from the destination terminal, e.g., a single bit indicating the success or failure of the direct transmission. If the destination provides a negative acknowledgment via feedback; in this case only, the relay retransmits in an attempt to exploit spatial diversity by combining the signals that the destination receives from the source and the relay. In this paper, we study the end-to-end performance of incremental relaying cooperative-diversity networks using decode-and-forward relays over independent non-identical Rayleigh fading channels. Closed-form expressions for the bit error rate and the signal-to-noise ratio (SNR) outage probability are determined. Results show that the incremental relaying cooperative diversity can achieve the maximum possible diversity, compared with the regular cooperative-diversity networks, with higher throughput.