The communication model typically assumed in wireless ad-hoc networks is based on a traditional "pipelined relay" (PR) strategy. In PR, an end-to-end flow has multiple outstanding packets (or data units) along the path from the source to the destination. In this paper, we argue that due to several unique properties of wireless ad-hoc networks, PR can be fundamentally improved upon. We present a new non-pipelined relay (nPR) strategy, where end-to-end flows have exactly one outstanding packet (or data unit) along the end-to-end path. We show that nPR has the following properties: (i) Under idealized network conditions, it provides performance improvement, in terms of end-to-end throughput capacity and network transport capacity over PR, and achieves proportional fairness; and (ii) Under practical network conditions, it further increases the above performance improvements, both in terms of the throughput achieved, and in terms of the fairness between flows. Finally, we present a forwarding protocol that practically realizes nPR. Through analysis and ns2 based packet level simulations, we evaluate the performance of the proposed strategy, and that of the forwarding protocol.