This paper introduces an empirical strategy to estimate dynamic treatment effects in randomized trials that provide treatment in multiple stages and in which various noncompliance problems arise, such as attrition and selective transitions between treatment and control groups. Our approach is applied to the highly influential four-year randomized class size study, Project STAR. We find benefits from attending small classes in all cognitive subject areas in kindergarten and first grade. We do not find any statistically significant dynamic benefits from continuous treatment versus never attending small classes following grade 1. Finally, statistical tests support accounting for both selective attrition and noncompliance with treatment assignment.