Protocols designed to provide error-free communications over lossy links commonly employ the idea of sliding windows, which is based on the Go-Back-N automatic repeat request (ARQ) scheme. Unless the packet error rate is extremely small, this scheme is known to perform poorly in connections with high bandwidth and round-trip delay. The methods typically used to address this drawback, such as selective repeat (SR) feedback and forward error correction (FEC), carry a cost in terms of memory requirements (e.g. buffers for out-of-order packets), implementation complexity, and extra computation time, and therefore energy consumption. While this is not a major consideration in traditional wired networks, it implies that such methods are unsuitable for certain applications involving wireless devices with severe resource limitations, e.g. in sensor networks. In this work, we focus on low-key bufferless receivers, incapable of accepting out-of-order packets or decoding FEC codes; consequently, the only possible way to increase the throughput efficiency above that of the Go-Back-N scheme is by advance packet retransmission. We carry out a detailed study of the fundamental performance bounds achieveable by advance retransmission strategies, show that schemes based on a fixed number of packet repetitions are suboptimal, and describe a novel heuristic approach, called Maximum Expected Advance First, which is shown to be asymptotically optimal and attain a significant throughput gain over Go-Back-N, without requiring any enhancements or additional resources at the receiver.