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Backoff algorithms can be employed on point-to-point wireless fading links to improve energy efficiency., particularly when the link experiences long deep fades and bursty errors. A backoff scheme at the link layer (LL), applying an appropriate backoff rule upon each LL packet loss event due to channel errors, can intentionally leave the channel idle (i.e., not transmit) for some specified number of slots, thereby reducing the possible energy wastage due to packet transmissions in error. Our new contribution in this paper is that we consider the use of backoff algorithms on wireless fading links with large round-trip delays, propose a go-back-N (GBN) protocol with backoff, and present a renewal-reward analysis of the throughput and energy efficiency performance of the proposed scheme. We show that the GBN protocol with a linear backoff (LBO) strategy results in energy savings of about 2 dB compared to GBN with no backoff (NBO), even in the case of large round-trip delays. In addition, we also propose and analyze an adaptive go-back-N/stop-and-wait (GBN/SAW) ARQ scheme with LL backoff. We show that this scheme with LBO achieves energy efficiency performance quite close to that of an ideal (though not practical) backoff scheme which assumes a priori knowledge of the channel status in each slot.