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Concerned about the low academic ability of public school teachers, in the 1990s and 2000s, some states increased licensing stringency to weed out low-quality candidates, while others decreased restrictions to attract high-quality candidates. We offer a theoretical model justifying both reactions. Using data from 1991-2007 on licensing requirements and teacher quality - as measured by the selectivity of teachers' undergraduate institutions - we find that stricter licensing requirements, especially those emphasizing academic coursework, increase the left tail of the quality distribution for secondary school teachers without significantly decreasing quality for high-minority or high-poverty districts.