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Random hypothesis generation is integral to many robust geometric model fitting techniques. Unfortunately, it is also computationally expensive, especially for higher order geometric models and heavily contaminated data. We propose a fundamentally new approach to accelerate hypothesis sampling by guiding it with information derived from residual sorting. We show that residual sorting innately encodes the probability of two points having arisen from the same model, and is obtained without recourse to domain knowledge (e.g., keypoint matching scores) typically used in previous sampling enhancement methods. More crucially, our approach encourages sampling within coherent structures and thus can very rapidly generate all-inlier minimal subsets that maximize the robust criterion. Sampling within coherent structures also affords a natural ability to handle multistructure data, a condition that is usually detrimental to other methods. The result is a sampling scheme that offers substantial speed-ups on common computer vision tasks such as homography and fundamental matrix estimation. We show on many computer vision data, especially those with multiple structures, that ours is the only method capable of retrieving satisfactory results within realistic time budgets.