This letter aims to solve the power minimization problem for interference-free OFDM systems under achievable throughput and spectral mask constraints. To this end, we use a general analytic formula to yield an efficient initial bit vector, i.e., given a total number of bits, the total power use corresponding to an efficient bit vector is minimum. We propose a low-complexity algorithm that achieves the global optimum of the problem. We theoretically prove that the number of bits required to add/remove, starting from the efficient initial bit vector, is upper bounded by the sum of half the number of active subcarriers and an arbitrary tolerance value. Simulation results show that the total power consumption is minimized with significant reduction of the computation cost as compared to other optimum algorithms.