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An optimal power and rate scheduling problem for a single user transmitting to a base station on a fading wireless link with the objective of minimizing the mean delay subject to an average power constraint is considered. The base station acts as a controller which, depending upon the transmitter buffer lengths and the signal power to interference ratio (SIR) on the uplink pilot channel, allocates transmission rate and power to the user. We provide structural results for an average cost optimal stationary policy under a long run average transmitter power constraint. We obtain a closed form expression relating the optimal policy when the SIR is the best, to the optimal policy for any other SIR value. We also obtain lower and upper bounds for the optimal policy.