Model order selection and cue combination are both difficult open problems in the area of clustering. In this work we build upon stability-based approaches to develop a new method for automatic model order selection and cue combination with applications to visual grouping. Novel features of our approach include the ability to detect multiple stable clusterings (instead of only one), a simpler means of calculating stability that does not require training a classifier, and a new characterization of the space of stabilities for a continuum of segmentations that provides for an efficient sampling scheme. Our contribution is a framework for visual grouping that frees the user from the hassles of parameter tuning and model order selection: the input is an image, the output is a shortlist of segmentations.