Digital contact-tracing applications (DCTAs) can control the spread of epidemics, like the COVID-19 pandemic. But people in Western societies fail to accept DCTAs. Understanding the low acceptance is key to policymakers who support DCTAs to avoid harsh nationwide lock-downs. In a preregistered study in a representative Swiss sample(N=757), we compare the role of individual risk perception, risk preferences, social preferences, and social values in the acceptance of and compliance with DCTA. The results show a low acceptance of DCTAs but high compliance with the measures recommended by DCTAs. Risk preferences and perceptions, but not social preferences, influenced accepting DCTAs; a high health risk perception and a low data-security risk perception increased acceptance. Additionally, supporting political measures, technical abilities, and understanding the DCTA functionality had large effects on accepting DCTAs. Therefore, we recommend highlighting personal health risks and clearly explaining DCTAs, focusing on data security, to enhance DCTA acceptance.