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We propose a system that finds the strongest supporting evidence for a given answer to a question, using passage-based question-answering (QA) as a testbed. We train evidence agents to select the passage sentences that most convince a pretrained QA model of a given answer, if the QA model received those sentences instead of the full passage. Rather than finding evidence that convinces one model alone, we find that agents select evidence that generalizes; agent-chosen evidence increases the plausibility of the supported answer, as judged by other QA models and humans. Given its general nature, this approach improves QA in a robust manner: using agent-selected evidence (i) humans can correctly answer questions with only ~20% of the full passage and (ii) QA models can generalize to longer passages and harder questions.