At the beginning of the COVID-19 pandemic, high hopes were placed on digital contact tracing. Digital contact tracing apps can now be downloaded in many countries, but as further waves of COVID-19 tear through much of the northern hemisphere, these apps are playing a less important role in interrupting chains of infection than anticipated. We argue that one of the reasons for this is that most countries have opted for decentralised apps, which cannot provide a means of rapidly informing users of likely infections while avoiding too many false positive reports. Centralised apps, in contrast, have the potential to do this. But policy making was influenced by public debates about the right app configuration, which have tended to focus heavily on privacy, and are driven by the assumption that decentralised apps are “privacy preserving by design”. We show that both types of apps are in fact vulnerable to privacy breaches, and, drawing on principles from safety engineering and risk analysis, compare the risks of centralised and decentralised systems along two dimensions, namely the probability of possible breaches and their severity. We conclude that a centralised app may in fact minimise overall ethical risk, and contend that we must reassess our approach to digital contact tracing, and should, more generally, be cautious about a myopic focus on privacy when conducting ethical assessments of data technologies.