In this letter, a novel low complexity bit and power loading algorithm is formulated for multicarrier communication systems. The proposed algorithm jointly maximizes the throughput and minimizes the transmit power through a weighting coefficient $α$, while meeting constraints on the target bit error rate (BER) per subcarrier and on the total transmit power. The optimization problem is solved by the Lagrangian multiplier method if the initial $α$ causes the transmit power not to violate the power constraint; otherwise, a bisection search is used to find the appropriate $α$. Closed-form expressions are derived for the close-to-optimal bit and power allocations per subcarrier, average throughput, and average transmit power. Simulation results illustrate the performance of the proposed algorithm and demonstrate its superiority with respect to existing allocation algorithms. Furthermore, the results show that the performance of the proposed algorithm approaches that of the exhaustive search for the discrete optimal allocations.