This study explores the challenges of reporting societal impacts for ex post evaluation purposes. Our starting point are the challenges researchers meet when writing about narrative impact cases. We introduce a distinction between the factual and rhetorical components of impact arguments. With this, we highlight how a focus on societal impacts as effects, in combination with requirements to support impacts with evidence, sets limits to the reporting on impacts. We apply this distinction in an empirical analysis of impact case studies submitted by sociologists to Research Excellence Framework (REF2014) in the United Kingdom and to Sameval 2018 in Norway, and we highlight the challenges researchers face in building arguments regarding instrumental, conceptual and symbolic impacts. Based on our findings, sociologists encounter problems specifically in evidencing conceptual impacts, that are claimed to generate the most profound changes in society. In building causality and credibility into the cases, the ultimate challenge remains: Indirect, non-linear and diffuse impacts are too vague to be captured in a concrete manner.