In wireless access systems, there has been much interest in enhancing the performance of orthogonal frequency division multiplexing (OFDM) in a frequency selective fading channel. If the channel is static and is perfectly known to both the transmitter and the receiver, the water-filling technique with adaptive modulation is known to be optimal . However, this requires intensive traffic overheads for reporting channel state information on all subcarriers. In this paper, we consider an adaptive modulation and coding scheme for bit-interleaved coded OFDM with reduced feedback information satisfying a specified quality of service level. We propose a rate adaptation scheme which utilizes the estimated bit error rate for supportable transmission rates. In this scheme, a user equipment chooses the best modulation and coding scheme (MCS) level based on one OFDM symbol rather than on the whole subcarriers, then the user needs to send back only the selected MCS level index. The proposed scheme does not require the water-filling procedure and the amount of the feedback reduces to a single integer value irrespective of the number of subcarriers. Simulation results show that the proposed scheme can significantly reduce the system complexity while minimizing the performance loss compared to the optimum water-filling scheme.