This paper investigates how the precision and stability of a teacher's value-added estimate relates to the characteristics of the teacher's students. Using a large administrative data set and a variety of teacher value-added estimators, it finds that the stability over time of teacher value-added estimates can depend on the previous achievement level of a teacher's students. The differences are large in magnitude and statistically significant. The year-to-year stability level of teacher value-added estimates are typically 25% to more than 50% larger for teachers serving initially higher performing students compared to teachers with initially lower performing students. In addition, some differences are detected even when the number of student observations is artificially set to the same level and the data are pooled across two years to compute teacher value-added. Finally, the paper offers a policy simulation which demonstrates that teachers who face students with certain characteristics may be differentially likely to be the recipient of sanctions in a high stakes policy based on value-added estimates and more likely to see their estimates vary from year-to-year due to low stability.