Transparent motions can be isolated in the Fourier domain, using derivative prefilters that selectively null the spatio-temporal energy consistent with the gradient constraint imposed by each component velocity. We use these ``nulling'' prefilters to robustly compute the support a particular velocity has at a point despite other velocities that may also be present at that point. Images are decomposed into a set of global constraints that account for a maximal amount of the motion information in the sequence. Adopting global motion hypotheses and a selection mechanism based on finding a parsimonious subset of these hypotheses, we show results separating motion stimuli into their constituent layers, even when those layers are transparently combined in the stimuli.