One of the many problems posed by the collective effort to tackle COVID-19 is non-compliance with restrictions. Some people would like to obey restrictions but cannot due to their job or other life circumstances; others are not good at following rules that restrict their liberty, even if the potential consequences of doing so are repeatedly made very clear to them. Among this group are a minority who simply do not care about the consequences of their actions. But many others fail to accurately perceive the harms that they might be causing. One of the main reasons for this is that the harms done by transmitting COVID-19 to someone else are morally distant from the agent, particularly in cases where infection is asymptomatic. In this paper, I describe seven different aspects of moral distance in the context of COVID-19, explore how they affect (lack of) motivation to obey restrictions, and suggest several ways in which such moral distance can be reduced - primarily through enhanced-contact tracing that makes it clear to individuals and the public precisely who they could be harming and how.