Migrant health advantages, the ‘healthy immigrant effect’, erode over time, leading to what is known as unhealthy assimilation. Health-related behaviours are central to unhealthy assimilation, and here we focus on an understudied and central part of our daily time: sleep. Building on diverse streams of literature, we conceptualize and empirically study the sleep assimilation patterns of immigrants. With data from Germany, we demonstrate that immigrants sleep significantly more than natives upon arrival, while their sleep ‘advantage’ dissipates with years spent in the host country. We also explore the heterogeneity of the sleep assimilation process by gender, education, wages, work schedules, and job physical intensity.