Mental health problems are increasing among young adults, and growing evidence points to social media platforms as a potential influence. Design decisions made by platform developers have the potential to fundamentally impact mental well-being. However, translating abstract values such as “well-being” or “mental health” into concrete norms and design features is challenging. We explore the potential of using a value sensitive design approach towards redesigning a social media environment that promotes mental well-being. We interviewed social media experts, held a focus group with adolescent users, and created a values hierarchy that translates abstract well-being values into norms and design requirements. Results reveal that mental well-being is negatively impacted by the inherent value tensions found in the design of social media platforms, tensions such as authenticity and connection, personalization and autonomy, and control and autonomy. We propose a value-sensitive design approach, informed by involving young users and other stakeholders, to show how to integrate key values into social media redesign.