Performance assessment is permeating increasingly diverse domains of higher education, even in areas previously perceived to be too complex and idiosyncratic to quantify. The UK's attempts to assess 'research impact' within the Research Excellence Framework (REF) are illustrative of this trend and are being closely monitored by several other countries. A fundamental rationale for employing narrative case studies to assess impact within REF, rather than taking a (less resource intensive) quantified approach, was that this would allow for the variation, complexity and idiosyncrasy inherent in research impact. This paper considers whether this promise of narrative flexibility has been realised, by analysing a combination of REF impact case study reports and interviews and focus group discussions with actors involved in case study production. Informed by this analysis, our central argument is that the very quality which allows narratives to govern is their ability to standardise performance (albeit whilst retaining a degree of flexibility). The paper proposes that REF impact case studies position narratives of impact as technologies of governance in ways that restrict the 'plot line' and belie the far more complex accounts held by those working to achieve research impact. This is partly because, as research impact becomes institutionalised within universities' measurement infrastructures, higher education institutions become impact gatekeepers, filtering out narratives that are deemed overly complex or insufficiently persuasive, while perpetuating particular approaches to recounting tales of impact that are deemed likely to perform well. Crucially, these narratives not only describe impact but actively construct it as an auditable phenomenon.