In this paper, the subcarrier, bit, and power allocation problem for minimizing total transmit power in multiuser OFDM systems is considered and a near-optimal allocation scheme is developed. The heuristic algorithms based on initial subcarrier assignment and iterative improvement two steps have been proposed by Wong et al. and Chen et al. for real-time services [4- 5]. However, an appropriate method for the initial assignment should be selected or designed to offer even better performance. In this paper, one subcarrier allocation algorithm proposed by Zhang  is adopted as an initial subcarrier assignment method for the allocation problem. Its advantage is that there is no need to pre-determine the number of the assigned subcarriers for each user, and it outperforms the constructive initial assignment method proposed by Wong et al.. We adopt the subcarrier allocation algorithm proposed by Zhang along with iterative improvement schemes to obtain better performance. Detailed discussions of the subcarrier allocation algorithm proposed by Zhang are presented in this paper. As indicated in the simulation results, it reveals that the better initial subcarrier assignment with the iterative improvement schemes achieves better performance. We utilize the linear integer programming-based branch-and-bound algorithm to provide the optimum solution as the performance bound. The simulation results show that the performance is improved with the new proposed heuristic polynomial time algorithm and is close to that of the optimum solution.