This paper presents a case study of a Spanish university that sheds light on the precarious nature of many academic posts. It looks at how women academics build their careers in the current neoliberal university, which measures scholarly output through the indexing metric. Application of this yardstick renders many academic careers all the more precarious because it fails to take into account women's care commitments. Because the issue is 'hidden', it is one that is hard to remedy. Based on a quantitative and qualitative methodology, the study's empirical data revealed that the neoliberal university discriminates against women by overlooking the care burden they bear. We conclude that needs to base itself on non-androcentric principles in which care is a key component. This would avoid academia penalizing those people who either require or provide care -- especially women.