Standard predictive multiple suppression techniques in marine reflection seismology usually resort to one-dimensional assumptions about the underlying earth model. The methods presented here use a multiple model which assumes vertical incidence propagation in the water layer, yet relaxes common assumptions of zero offset and zero dip. In particular, different reflectivities and water depths are assumed at source and receiver locations.One of these methods, seafloor-consistent multiple suppression, models each seismic trace as a convolution of an average frequency response with anomalous shot, geophone, midpoint, and offset responses. In the log-frequency domain, this becomes a separable, additive model which can be solved by linear least-squares techniques. The anomalous amplitude responses are solved for each frequency in 'shot-receiver' space with frequency as the outer loop of the algorithm.Once the seismic data set has been resolved into average and anomalous amplitude responses, the multiple reverberation response is identified with the product of the anomalous shot and geophone responses. Since one can argue on physical grounds that the reverberation response for any particular trace must be minimum phase, it suffices to solve only for amplitude responses and ignore phase contributions.The methods are applied to a deep water marine seismic line from the Flemish Cap area of the Labrador Sea with extremely encouraging results.