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In this letter, we are concerned with adaptive ARQ techniques combined with backoff strategies that exploit the bursty nature of wireless links for improved energy savings. Specifically, we propose an adaptive Go-back-N/Stop-and-Wait (GBN/SAW) 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) on highly correlated fading channels when the round-trip delays (RTD) are small, and this energy saving decreases as RTD increases. With adaptive GBN/SAW protocol with LBO, however, the energy saving is retained high even for large RTDs. In fact, the proposed adaptive GBN/SAW protocol with LBO performs quite close to that of an ideal (though not practical) backoff scheme which assumes a priori knowledge of the channel status in each slot.