Successful removal of coherent-noise sources greatly determines seismic imaging quality. Major advances have been made in this direction, e.g., surface-related multiple elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors, and clutter in predicted signal components can be detrimental. Adopting a Bayesian approach, along with assuming approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes predictions produced by, for example, SRME as input and separates these components in a robust manner. In addition, the proposed algorithm controls the energy mismatch between separated and predicted components. Such a control, lacking in earlier curvelet-domain formulations, improves results for primary-multiple separation on synthetic and real data.