Digital contact-tracing applications (DCTAs) can help control the spread of epidemics, such as the coronavirus disease 2019 pandemic. But people in Western societies fail to install DCTAs. Understanding the low use rate is key for policy makers who support DCTAs as a way to avoid harsh nationwide lockdowns. In a preregistered study in a representative German-speaking Swiss sample (N = 757), the roles of individual risk perceptions, risk preferences, social preferences, and social values in the acceptance of and compliance with DCTA were compared. The results show a high compliance with the measures recommended by DCTAs but a comparatively low acceptance of 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, support of 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.