The apparent early success in China's large-scale intervention to control the COVID-19 epidemic has led to interest in whether other countries can replicate it as well as concerns about a resurgence of the epidemic if or when China relaxes the interventions. In this paper we look at the impact of a single short-term intervention on an epidemic. We see that if an intervention cannot be sustained long-term, it has the greatest impact if it is imposed once infection levels have become large enough that there is an appreciable number of infections present. For minimising the total number infected it should start close to the peak so that there is no rebound once the intervention is stopped, while to minimise the peak prevalence, it should start earlier, allowing two peaks of comparable size rather than one very large peak. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each sub-population separately.We do not attempt to clearly determine what makes an intervention sustainable or not. We believe that is a policy question. If an intervention is sustainable, it should be kept in place. Our intent is to offer insight into how best to time an intervention whose impact on society is too great to maintain.