The modern omnipresence of social media and social networking sites (SNSs) brings with it a range of important research questions. One of these concerns the impact of SNS use on mental health and well-being, a question that has been pursued in depth by scholars in the psychological sciences and the field of human-computer interaction. Despite this attention, the design choices made in the development of SNSs and the notion of well-being employed to evaluate such systems require further scrutiny. In this viewpoint paper, we examine the strategic design choices made in our development of an enclosed SNS for young people experiencing mental ill-health in terms of ethical and persuasive design and in terms of how it fosters well-being. In doing so, we critique the understanding of well-being that is used in much of the existing literature to make claims about the impact of a given technology on well-being. We also demonstrate how the holistic concept of eudaimonic well-being and ethical design of SNSs can complement one another.