We investigated 2 engagement-fostering aspects of teachers' instructional styles--autonomy support and structure--and hypothesized that students' engagement would be highest when teachers provided high levels of both. Trained observers rated teachers' instructional styles and students' behavioral engagement in 133 public high school classrooms in the Midwest, and 1,584 students in Grades 9-11 reported their subjective engagement. Correlational and hierarchical linear modeling analyses showed 3 results: (a) Autonomy support and structure were positively correlated, (b) autonomy support and structure both predicted students' behavioral engagement, and (c) only autonomy support was a unique predictor of students' self-reported engagement. We discuss, first, how these findings help illuminate the relations between autonomy support and structure as 2 complementary, rather than antagonistic or curvilinear, engagement-fostering aspects of teachers' instructional styles and, second, the somewhat different results obtained for the behavioral versus self-report measures of students' classroom engagement. (Contains 2 footnotes, 2 tables, and 2 figures.)