This paper proposes a novel low complexity joint bit and power suboptimal allocation algorithm for multicarrier systems operating in fading environments. The algorithm jointly maximizes the throughput and minimizes the transmitted power, while guaranteeing a target bit error rate (BER) per subcarrier and meeting a constraint on the total transmit power. Simulation results are described that illustrate the performance of the proposed scheme and demonstrate its superiority when compared to the algorithm in [4] with similar or reduced computational complexity. Furthermore, the results show that the performance of the proposed suboptimal algorithm approaches that of an optimal exhaustive search with significantly lower computational complexity.