Recent philosophical literature has turned its attention towards assessments of how to judge scientific proposals as worthy of further inquiry. Previous work, as well as papers contained within this special issue, propose criteria for pursuitworthiness (Achinstein, 1993; Whitt, 1992; DiMarco & Khalifa, 2019; Laudan, 1977; Shan, 2020; Šešelja et al., 2012). The purpose of this paper is to assess the grounds on which pursuitworthiness demands can be legitimately made. To do this, I propose a challenge to the possibility of even (...) minimal criteria of pursuitworthiness, inspired by Paul Feyerabend. I go on to provide a framework for identifying the contexts in which pursuitworthiness criteria may promote the efficiency of scientific inquiry. I then spell out some implications this framework has for values and pursuit. (shrink)