The modified one-bit transform (M1BT) motion-estimation method efficiently combines the low-complexity 1BT algorithm and the high-accuracy full search algorithm. As a result, it provides a good tradeoff between performance and computational complexity. The search range scheme in the M1BT method, however, is somewhat inefficient. A proposal was made for a new search range scheme that efficiently increases the search range without increasing the computational complexity. The proposed method also makes use of statistical data to reduce the number of search points. By using both the new search range scheme and the new search strategy, the proposed method not only reduces the complexity, but also improves the performance. The proposed method can be easily extended to similar methods, such as the modified two-bit transform (M2BT) and modified constrained 1BT (MC1BT) methods.