We present an efficient bit allocation algorithm for multicarrier systems operating in frequency-selective environment. The proposed algorithm strives to maximize the overall throughput while guaranteeing that the mean bit error rate (BER) remains below a prescribed threshold. The algorithm is compared with several other algorithms found in literature in terms of the overall throughput, mean BER, and relative computational complexity. Furthermore, the algorithms are compared with an exhaustive search routine to determine the optimal bit allocation in terms of maximizing throughput given the constraint on error performance. No power allocation is performed by the algorithms. Results show that the proposed algorithm has approximately the same throughput and mean BER as the optimal solution while possessing a significantly lower computational complexity relative to the other algorithms with similar performance. When compared to algorithms which employ approximations to waterfilling, the computational complexity is comparable while the overall throughput is closer to the optimum.