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We improve upon pairwise annotation for active learning in coreference resolution, by asking annotators to identify mention antecedents if a presented mention pair is deemed not coreferent. This simple modification, when combined with a novel mention clustering algorithm for selecting which examples to label, is much more efficient in terms of the performance obtained per annotation budget. In experiments with existing benchmark coreference datasets, we show that the signal from this additional question leads to significant performance gains per human-annotation hour. Future work can use our annotation protocol to effectively develop coreference models for new domains. Our code is publicly available at https://github.com/belindal/discrete-active-learning-coref .