The presence of internal multiples in seismic data can lead to artifacts in subsurface images obtained by conventional migration algorithms. This problem can be ameliorated by removing multiples prior to migration, if they can be reliably estimated. Recent developments have renewed interest in the plane-wave domain formulations of the inverse-scattering series (ISS) internal multiple prediction algorithms. We have built on this by considering sparsity-promoting plane-wave transforms to minimize artifacts and in general improve the prediction output. Furthermore, we argue for the use of demigration procedures to enable multidimensional internal multiple prediction with migrated images, which also facilitate compliance with the strict data completeness requirements of the ISS algorithm. We assert that a combination of these two techniques, sparsity-promoting transforms and demigration, paves the way for a wider application to new and legacy data sets.