Data activism, promoting new forms of civic and political engagement, has emerged as a response to problematic aspects of datafication that include tensions between data openness and data ownership, and asymmetries in terms of data usage and distribution. In this article, we discuss MyData, a data activism initiative originating in Finland, which aims to shape a more sustainable citizen-centric data economy by means of increasing individuals’ control of their personal data. Using data gathered during long-term participant-observation in collaborative projects with data activists, we explore the internal tensions of data activism by first outlining two different social imaginaries – technological and socio-critical – within MyData, and then merging them to open practical and analytical space for engaging with the socio-technical futures currently in the making. While the technological imaginary favours data infrastructures as corrective measures, the socio-critical imaginary questions the effectiveness of technological correction. Unpacking them clarifies the kinds of political and social alternatives that different social imaginaries ascribe to the notions underlying data activism, and highlights the need to consider the social structures in play. The more far-reaching goal of our exercise is to provide practical and analytical resources for critical engagement in the context of data activism. By merging technological and socio-critical imaginaries in the work of reimagining governing structures and knowledge practices alongside infrastructural arrangements, scholars can depart from the most obvious forms of critique, influence data activism practice, and formulate data ethics and data futures.