Around the world, governments have been asking their citizens to practice physical distancing and stay at home to contain the spread of Covid-19. Are happier people more willing to comply with these measures? Using three independent surveys covering over 119,000 adult respondents across 35 countries, including longitudinal data from the UK, we test competing psychological theories, and find that past and present happiness predicts compliance during lockdown. The relationship is stronger for those with higher levels of happiness. A negative mood, or loss in happiness, predicts lower compliance. We explore risk-avoidance and pro-social motivations for compliance, and find that these are not uniform but dependent on personal characteristics and context: people who are older or have certain medical preconditions seem to be predominantly motivated by risk-avoidance, whereas motivations of people who are less at risk of Covid-19 seem more mixed. Our findings have implications for policy design, targeting, and communication.