Most existing work in digital ethics is modeled on the "principlist" approach to medical ethics, seeking to articulate a small set of general principles to guide ethical decision-making. Critics have highlighted several limitations of such principles, including (1) that they mask ethical disagreements between and within stakeholder communities, and (2) that they provide little guidance for how to resolve trade-offs between different values. This paper argues that efforts to develop responsible digital health practices could benefit from paying closer attention to a different branch of medical ethics, namely public health ethics. In particular, I argue that the influential "accountability for reasonableness" (A4R) approach to public health ethics can help overcome some of the limitations of existing digital ethics principles. A4R seeks to resolve trade-offs through decision-procedures designed according to certain shared procedural values. This allows stakeholders to recognize decisions reached through these procedures as legitimate, despite their underlying disagreements. I discuss the prospects for adapting A4R to the context of responsible digital health and suggest questions for further research.