This paper explores the relationship between teacher testing and teacher effectiveness using a unique dataset that links teachers to their individual students. My findings show a positive relationship between some teacher licensure tests and student achievement. But they also suggest that states face significant tradeoffs when they require particular performance levels as a precondition to becoming a teacher: some teachers whom we might wish were not in the teacher workforce based on their contribution toward student achievement are eligible to teach based on their performance on these tests, while other individuals who would be effective teachers are ineligible. (Contains 4 tables, 1 figure and 25 footnotes.)