Some educators are concerned that students with test scores at the bottom or top of the test score distribution will negatively affect the value-added estimates of teachers of those students. Using data from a large urban district, this working paper finds that test scores at the floor contain real information about students' performance, because students who score at the floor in one year score at or near the bottom of the scale, on average, in other years. For test score ceilings, the study finds that the lower the ceiling, the more the value-added estimates tend to shrink toward the average teacher, because test scores at the ceiling contain imprecise information about students' achievement.