This paper considers bit-loading algorithms to maximize throughput under total power and spectral mask constraints in interference-free OFDM systems. The contribution is twofold. First, we propose a simple criterion to switch between two wellknown algorithms from the literature: the conventional Greedy and Greedy-based bit-removing (with maximum allowable bit loading initialization) algorithms. Second, we present a new lowcomplexity loading algorithm that exploits the bit vector obtained by rounding the water-filling algorithm solution to the associated continuous-input rate maximization problem as an efficient initial bit vector of the Greedy algorithm.We theoretically prove that this bit vector has two interesting properties. The first one states that it is an efficient bit vector, i.e., there is no movement of a bit from one subcarrier to another that reduces the total used power. The second one states that the optimized throughput, starting from this initial bit vector, is achieved by adding or removing bits on each subcarrier at most once. Simulation results show the efficiency of the proposed algorithm, i.e., the achievable throughput is maximized with significant reduction of computation cost as compared to many algorithms in the literature.