Constitutive mechanistic explanations are said to refer to mechanisms that constitute the phenomenon-to-be-explained. The most prominent approach of how to understand this constitution relation is Carl Craver’s mutual manipulability approach to constitutive relevance. Recently, the mutual manipulability approach has come under attack (Leuridan 2012; Baumgartner and Gebharter 2015; Romero 2015; Harinen 2014; Casini and Baumgartner 2016). Roughly, it is argued that this approach is inconsistent because it is spelled out in terms of interventionism (which is an approach to causation), whereas constitutive relevance is said to be a non-causal relation. In this paper, I will discuss a strategy of how to resolve this inconsistency, so-called fat-handedness approaches (Baumgartner and Gebharter 2015; Casini and Baumgartner 2016; Romero 2015). I will argue that these approaches are problematic. I will present a novel suggestion of how to consistently define constitutive relevance in terms of interventionism. My approach is based on a causal interpretation of mutual manipulability, where manipulability is interpreted as a causal relation between the mechanism’s components and temporal parts of the phenomenon.