Course-based undergraduate research experiences (CUREs) provide a promising avenue to attract a larger and more diverse group of students into research careers. CUREs are thought to be distinctive in offering students opportunities to make discoveries, collaborate, engage in iterative work, and develop a sense of ownership of their lab course work. Yet how these elements affect students' intentions to pursue research-related careers remain unexplored. To address this knowledge gap, we collected data on three design features thought to be distinctive of CUREs (discovery, iteration, collaboration) and on students' levels of ownership and career intentions from ~800 undergraduates who had completed CURE or inquiry courses, including courses from the Freshman Research Initiative (FRI), which has a demonstrated positive effect on student retention in college and in science, technology, engineering, and mathematics. We used structural equation modeling to test relationships among the design features and student ownership and career intentions. We found that discovery, iteration, and collaboration had small but significant effects on students' intentions; these effects were fully mediated by student ownership. Students in FRI courses reported significantly higher levels of discovery, iteration, and ownership than students in other CUREs. FRI research courses alone had a significant effect on students' career intentions.