Despite practices addressing disability in design and advocating user-centered design (UCD) approaches, popular mainstream technologies remain largely inaccessible for people with disabilities. We conducted a design course study investigating how student designers regard disability and explored how designing for both disabled and non-disabled users encouraged students to think about accessibility throughout the design process. Students focused on a design project while learning UCD concepts and techniques, working with people with and without disabilities throughout the project. We found that designing for both disabled and non-disabled users surfaced challenges and tensions in finding solutions to satisfy both groups, influencing students' attitudes toward accessible design. In addressing these tensions, non-functional aspects of accessible design emerged as important complements to functional aspects for users with and without disabilities.