This paper explores the traditional distinction between problem- and possibility-driven design for promoting user well-being. Problem-driven design identifies and addresses unfulfilled needs to reduce ill-being (i.e., the first space of design for well-being), while possibility-driven design seeks to enhance well-being without addressing existing problems (i.e., the second space of design for well-being). The latter is informed by positive psychology, which studies the conditions for human flourishing. Although possibility-driven design has added a valuable new focus to the design repertoire, it confronts designers with some key challenges that are currently unresolved. Examples of these challenges include finding focus, determining evaluation metrics, and convincing stakeholders. To address these issues, this paper introduces a third space of design for well-being that integrates the two approaches with the intention of combining their strengths. The paper begins by discussing the first two spaces, then introduces the ideas behind the third space, and presents a design case of the third space in action. The case involves a design that supports the well-being of people engaging in online dating. The case is used as a platform to explore and discuss the strengths and weaknesses of the third space, and possible future applications of the integrated approach to design for well-being.