What is the most efficient way to respond to recessions in the labor market? To this question, policymakers on the two sides of the pond gave diametrically opposed answers during the COVID-19 crisis. In the United States, the focus was on insuring workers by increasing the generosity of unemployment insurance. In Europe, instead, policies were concentrated on saving jobs, with the expansion of short-time work programs to subsidize labor hoarding. Who got it right? In this article, we show that far from being substitutes, unemployment insurance and short-time work exhibit strong complementarities. They provide insurance to different types of workers and against different types of shocks. Short-time work can be effective at reducing socially costly layoffs against large temporary shocks, but it is less effective against more persistent shocks that require reallocation across firms and sectors. We conclude that short-time work is an important addition to the labor market policy-toolkit during recessions, to be used alongside unemployment insurance.