This paper considers the likely shape of the next UK Research Excellence Framework (REF). It explores some of the recommendations from the 2016 Stern Review (those concerned with "outputs") and their envisaged impact on the exercise. Drawing on lessons learnt from the previous round of the REF, and some wider commentary, the paper considers some of the problems emergent from REF2014, whether they can be mitigated, and whether new problems might emerge in REF2021. Prominently, the issues of "burden" and "gaming" are explored. Although there are some grounds for optimism, much more detail will be needed before we can be reasonably confident about achieving a less burdensome and a more accurate evaluation of research "quality" within universities across the UK.