Abstract This article aims to provide a concise overview of the most relevant topics concerning the implementation of acceptability judgments in generative research. The first part focuses on theoretical issues, including the reasons underlying the prevalence of acceptability judgments, the skepticism towards the wide use of informal judgments, the arguments for and against the continued use of informal data points and the challenges related to experimental data collection and the gradient nature of judgments. The second part further explores the concept of gradient acceptability and its different sources. We suggest that violations of soft constraints correspond with partial acceptability, unlike violations of hard constraints, which cause strong unacceptability. Based on our investigation of selected partially acceptable syntactic phenomena in Polish, we show that their syntactic accounts can also benefit from the inclusion of non-syntactic factors, which can be more reliably identified via experimental methodology. More specifically, we propose that (i) the lack of subject orientation of pronominal possessives could be attributed to lexical ambiguity, (ii) coreference of possessive cataphora is facilitated by antecedent backgrounding and (iii) WCO is improved by focus marking of the possessive pronoun, (iv) while processing of the last two structures could be ameliorated with more informative fillers.