The standard approach to protecting privacy in healthcare aims to control access to personal information. We cannot regain control of information after it has been shared, so we must restrict access from the start. This ‘control’ conception of privacy conflicts with data-intensive initiatives like precision medicine and learning health systems, as they require patients to give up significant control of their information. Without adequate alternatives to the control-based approach, such data-intensive programmes appear to require a loss of privacy. This paper argues that the control view of privacy is shortsighted and overlooks important ways to protect health information even when widely shared. To prepare for a world where we no longer control our data, we must pursue three alternative strategies: obfuscate health data, penalise the misuse of health data and improve transparency around who shares our data and for what purposes. Prioritising these strategies is necessary when health data are widely shared both within and outside of the health system.