The article explores the mechanisms affecting people's perceived ability to influence the uneven power relationships between them and data-driven companies that collect, store, analyze, and use their data and information. I first present a study in which participants were asked to use innovative privacy enhancing technology, enabling them to claim a form of ownership over their personal data and information. This study shows that new socio-technical developments can reduce the uneven balance of power between individuals who disclose personal data and information and the companies which collect, store, and deploy that information. Based on these findings, I point to modes of operation and regulation that could assist data subjects in gaining more control over the relationships between them and companies. The article concludes with suggestions of ethical measures that may aid individuals to influence the ‘give and take’ relationship with data-driven companies.