We propose a category-independent method to produce a bag of regions and rank them, such that top-ranked regions are likely to be good segmentations of different objects. Our key objectives are completeness and diversity: Every object should have at least one good proposed region, and a diverse set should be top-ranked. Our approach is to generate a set of segmentations by performing graph cuts based on a seed region and a learned affinity function. Then, the regions are ranked using structured learning based on various cues. Our experiments on the Berkeley Segmentation Data Set and Pascal VOC 2011 demonstrate our ability to find most objects within a small bag of proposed regions.