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In this paper, the problem of adaptive bit and power allocation for coded OFDM systems is considered. With emphasis on low feedback overhead and low complexity, we present a simple adaptive allocation technique, where data are transmitted only using the strongest subcarriers with uniform power and uniform constellation size. Due to the reduced number of used subcarriers, a fraction of coded bits are not transmitted, while keeping the information bit rate unchanged. The problem of bit and power allocation to minimize packet error rate (PER) reduces to determine the constellation size and the number of unused subcarriers. The optimal solution provides a good tradeoff among average SNR, coding gain, and demapping loss. To solve the problem, we introduce an effective SNR maximization approach. Numerical results show that the proposed scheme significantly improves PER performance.