Contact tracing apps have become one of the main approaches to control and slow down the spread of COVID-19 and ease up lockdown measures. While these apps can be very effective in stopping the transmission chain and saving lives, their adoption remains under the expected critical mass. The public debate about contact tracing apps emphasizes general privacy reservations and is conducted at an expert level, but lacks the user perspective related to actual designs. To address this gap, we explore user preferences for contact tracing apps using market research techniques, and specifically conjoint analysis. Our main contributions are empirical insights into individual and group preferences, as well as insights for prescriptive design. While our results confirm the privacy-preserving design of most European contact tracing apps, they also provide a more nuanced understanding of acceptable features. Based on market simulation and variation analysis, we conclude that adding goal-congruent features will play an important role in fostering mass adoption.