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We investigate performance aspects of adaptive modulation and scheduling as the amount of channel feedback is reduced. We study throughput, fairness and the sensitivity to incorrect channel quantizations. A main finding is that the throughput of a cellular downlink using strict multiuser diversity does not degrade significantly when the channel information is heavily quantized. On the other hand, unfairness increases and due to an inherent sensitivity to incorrectly chosen quantization levels there is a risk of occasional drastic performance drops. Noting that fixed-access schemes do not have the bad properties of multiuser diversity, but achieve unsatisfactory throughput, we propose a scheme combining the good aspects of multiuser diversity with the desirable properties of fixed access schemes. The result is a low-complexity scheduler and quantization policy that achieve large throughput gains as compared to fixed access without compromising fairness.