Aiming at minimizing the transmit power of orthogonal frequency-division multiplexing (OFDM) systems subject to the target data rate, the target bit error rate (BER), the maximum allowable power per subcarrier, and the maximum allowable size of constellations, we present a couple of new discrete bit-loading algorithms, named efficient bit filling (EBF) and efficient bit removal (EBR), which are based on our new idea of group-by-group bit filling. Both EBF and EBR perform bit loading in two stages and are able to converge to the optimal bit-allocation profile. In the first stage, an intermediate bit-allocation profile, which is tightly close to the final bit-allocation profile, is obtained by using our proposed group-by-group bit filling (for EBF) or group-by-group bit removal (for EBR). In the second stage, the well-known greedy bit filling (for EBF) or greedy bit removal (for EBR) is performed for the remaining bits (usually of a small size). Analytical and numerical results reveal that the proposed algorithms converge to the optimal bit allocation with much lower computational complexities than existing optimal algorithms. It is also shown that the proposed algorithms outperform typical suboptimal algorithms in power efficiency with relatively higher computational complexities.