This paper examines institutional change in father-specific leave - a centre-piece of the EU's work-life balance directive (WLBD) - from the perspective of gradual institutional change. The WLBD, a highly contentious directive, represents a litmus test for the possible impact of the European pillar of social rights (EPSR), on welfare state institutions, which are responsible for the organisation, financing and delivery of social rights in member states. The analysis comprises in-depth case studies in Denmark, Germany, France and Poland, with different combinations of family and parental leave policies prior to the WLBD. The findings reveal that the EU's directive is leading to convergence in paternity leave, but to divergence in parental leave. Our study is important because it shows that even if EU directives in social policy in principle can lead to upwards social convergence across the EU, when they are relatively weak in terms of precise constraint, for instance, for the level of remuneration for leave, this leads to differentiated integration. This could undermine the very purpose of the EPSR, which seeks to improve social rights for all citizens across the EU. Similar dynamics are likely to be present in other areas at the welfare state-labor market nexus, such as minimum wages or platform work, where the EU is also developing regulation under the auspices of the EPSR.