Modeling, which is the process of constructing, testing, and refining models, is an important skill in experimental physics, and thus a learning goal of many physics laboratory classes. One promising approach to help students develop modeling skills is to incorporate multiweek student-designed projects into lab courses. In order to assess the potential benefits of these projects in enhancing students' modeling abilities, we analyzed projects from three upper-division lab courses at different institutions. By looking at written student coursework and student interviews, we investigated which parts of the modeling process the students from each project undertook, and how this engagement in modeling differed depending on features of the projects. The projects in our dataset varied widely, showing evidence of different ways students engaged with model construction and revisions. We observed that the features of the projects, such as the goal of the project and the complexity of the required apparatus, were associated with the ways in which the students constructed models and enacted revisions. This has implications for how instructors may choose to frame and structure courses with student-designed lab projects.