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The variable nature of the wireless channel may cause the quality of service to be intolerable for certain applications. To combat channel variability, we consider rate adaptation at the physical layer. We build an adaptive communication system based on uncoded QAM in which the available information on the channel state is obtained using the mere packet-level ACK/NACK sequence. Our system chooses the constellation size that maximizes the expected packet level goodput for every single packet. Our simulations show that our system achieves a goodput reasonably close to the highest possible goodput achievable with full-feedback on Rayleigh-fading Markov channels.