This paper argues that the type of COVID-19 containment measures affects the trade-offs between infection cases, economic activity and sovereign risk. Using local projection methods and a year and a half of high-frequency daily data covering 44 advanced and emerging economies, we find that smart (e.g. testing) as opposed to physical (e.g. lockdown) measures appear to be best placed to tackle these trade-offs. Initial conditions also matter whereby containment measures can be less disruptive when public health response time is fast and public debt is low. We also construct a database of daily fiscal announcements for Euro area countries, and find that sovereign risk is improved under a combination of large support packages and smart measures.