Practical internal multiple prediction and removal is a high-priority area of research in seismic processing technology. Its significance increases in plays in which data are complex and sophisticated quantitative interpretation methods are apt to be applied. When the medium is unknown and/or complex, and moveout-based primary/multiple discrimination is not possible, inverse scattering-based internal multiple attenuation is the method of choice. However, challenges remain for its application in certain environments. For instance, when generators are widely distributed and are separated in space by a range of distances, optimum prediction parameters such as (which limits the proximity of events combined in the prediction) are difficult to determine. In some cases, we find that no stationary value of can optimally predict all multiples without introducing damaging artifacts. A reformulation and implementation in the time domain permits time nonstationarity to be enforced on , after which a range of possible data- and geology-driven criteria for selecting an schedule can be analyzed. The 1D and 1.5D versions of the time-nonstationary algorithm are easily derived and can be shown to add a new element of precision to prediction in challenging environments. Merging these ideas with multidimensional plane-wave domain versions of the algorithm provides 2D/3D extensions.