This paper discusses the application of adaptive modulation and adaptive rate turbo-coding to OFDM (orthogonal frequency-division multiplexing), to enable a closer approach to the Shannon capacity of the time and frequency selective channel. The adaptive turbo-code scheme is based on a subband adaptive method, and compares two adaptation algorithms: a conventional, conservative approach where modulation and code rate is chosen based on the poorest subcarrier in a subband, and an optimal approach based on a prediction of the average BER over all sub-carriers. Four modulation schemes (BPSK, QPSK, \8AMPM and 16QAM) and four code rates (1/3, 1/2, 2/3 and uncoded) are employed. Systems employing different numbers of combinations of these schemes are compared. Simulation results for throughput and BER show that 8 schemes are sufficient to approach the maximum capacity: a small reduction in throughput occurs with only 4 schemes (all 1/2 rate coded). The optimal adaptation algorithm provides a significant improvement.