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Maximizing the total rate with no coordination is an attractive option to increase the throughput of existing multiuser communication systems. This paper compares two sub-optimal methods for rate and power allocation in a two-user multicarrier channel with the optimum method, subject to individual power constraints. The two suboptimal methods, iterative water-filling (IW) and iterative constant-power transmission (ICP), closely approximate the performance of the optimum method when either interference-channel magnitude is smaller than the main-path gain or the total power budget is small. Both methods perform nearly alike and are easy to deploy in existing systems in which different transmission paths may not be coordinated.