One of the problems in OFDM system is that bit errors are normally concentrated in a few severely faded subcarriers, which therefore normally restrict the performance of the whole system. Adaptation algorithms are able to identify these subcarriers and improve the overall bit error rate of the whole OFDM frame by choosing different modulation schemes, code rates and other parameters for different subcarriers. Power allocation is another technique that can improve the performance of OFDM systems. A combination of a power allocation algorithm with the adaptive OFDM system is proposed in this paper to further improve performance. We determine the best possible power distribution over subcarriers for OFDM systems by power allocation algorithms, and choose modulation schemes and code rate for subcarriers using adaptation algorithms, and hence a better trade-off between the Bit error rate (BER) and throughput performance of OFDM system is achieved.