A new data-processing technique is presented which utilizes optimum multichannel digital filtering in conjunction with common subsurface horizontal stacking for the efficient rejection of multiple reflections. The method exploits the differential normal moveout between primary and multiple reflections that results from an increase in average velocity with depth. Triple subsurface coverage is obtained in the field; the common subsurface traces are individually prefiltered with different filters and stacked. The digital filters are designed on the least-mean-square-error criteria to preserve primaries (signal) in the presence of multiples (noise) of predictable normal moveout, and random noise. The method achieves wide-band separation of primary and multiple energy with only a three-point stack; it can work effectively with small normal moveout differences eliminating the need for long offsets and the attendant signal degradation due to wide-angle reflections; it does not require equal multiple moveout on the triplet of traces stacked; and finally the method is not sensitive to small errors in statics or predicted normal moveout. The technique is illustrated in terms of synthetic examples selected to encompass realistic field situations, and the parameter specification necessary for the multichannel filter design.