Focusing on the EU Code of Practice on Disinformation, this paper argues that European debates about regulating online disinformation need to be set against a broader perspective on regulating the digital environment as a public infrastructure. Occupying the grey area of legal but “harmful” content, disinformation is difficult to define, poorly understood, always evolving, and entangled in the fundamental right to freedom of expression. Self-regulatory mechanisms to increase the accountability of digital platforms, such as the EU Code, have repeatedly failed to address these core issues. Moreover, there is little evidence to suggest that the co-regulatory framework envisaged by the EU’s Digital Services Act will improve this situation. After reviewing these failures and weaknesses, this paper will suggest that policymakers can achieve better civic and democratic outcomes by focusing - not on a minority of large platforms and the content they host - but on regulating the digital environment as a public infrastructure through, for example, robust competition, data portability, and interoperability rules. Such actions have the potential to break the dominance of Big Tech while incentivising better and new services for citizens.