Switzerland has no formal research evaluation framework, and evaluation differs from institution to institution. Nevertheless, there are national discourses about research evaluation and about what, in other countries, is called “societal impact”. Drawing on interviews with higher education stakeholders, we show that the concept of “societal impact” has not gained ground in Switzerland. Rather, the science policy discourse revolves around the term “innovation”. The dual system in (higher) education in Switzerland leads to a clear distinction between applied and basic research; having a demonstrable impact on society is within the realm of the first of these. However, in a direct democracy such as Switzerland, civic functions of research influence the perception of academia, especially in the social sciences and humanities. The research-society nexus, however, is not perceived as something that can be captured by the idea of “societal impact” in any meaningful way. Creating public value rather than impact is at the heart of Swiss science policy.