Personal data spaces, or PDSs, are emerging intermediary services that allow users control over the sharing and use of their data. In this article, the surveillance capitalism model, which describes how businesses employ datafication to create value in the digital economy, is used to contextualize PDSs. Focusing on three PDS services, I analyze the social imaginaries they represent, paying attention to the increased agency over data they offer users. This proposed agency reflects the efforts of PDSs to intervene in, but not counter, surveillance capitalism. While their goal is to intensify datafication by increasing the quality and specificity of data that businesses can employ, their interventions also change the structure of data flows, allowing users to more directly benefit from datafication. PDSs envision their users as data-supplying and benefit-demanding market participants, active subjects in value creation instead of passive objects of data extraction. PDSs view themselves as platform providers that facilitate data exchanges and rely on market mechanisms to ensure beneficial services are developed for users to choose from.