According to a preferred aspect of the instant invention, there is provided herein a system and method for removing or attenuating multiples in datasets that is much more efficient than methods used heretofore. The increases in efficiency principally originate in two algorithmic advances. First, the instant inventors have improved the overall efficiency of the conventional SRME process by reordering the computations in a novel way. Second, the instant inventors have conceived and developed a faster method of computing the DMO transformation step that is often used as one component of the SMRE process, thereby increasing the efficiency of the multiple removal process even further.