While project-based learning purportedly values student agency, supporting and managing this remains challenging. We conducted a design-based research study to understand how problem authenticity, and task and participant structures can contribute to students' framing agency, in which students make decisions that are consequential to their learning through ill-structured problem framing. We compared three semesters of an undergraduate engineering design project (cohort 1 n=70; cohort 2 n=70; cohort 3 n=66). Discourse analysis of team talk highlights how task and participant structures supported students in the first and third cohorts to display framing agency. In contrast, cohort 2 displayed high agency over task completion, which they had framed as well-structured. We discuss implications for designing ill-structured learning in terms of participant and task structure and problem authenticity.