Why may an explanation, or more appropriately, the process of explaining, be relevant in a particular setting? This chapter argues that the explainability of AI can serve different instrumental and intrinsic purposes or values depending on the design context. Given these considerations, we ask how may developers design sXAI in such a way that it allows them to promote those values that are linked to the final purposes of deploying different AI systems in different contexts. To address this challenge, we turn to the widely used and discussed value-sensitive design (VSD) approach. First, the chapter provides a brief introduction to VSD and presents some points of criticism that have been raised in the literature—most notably, the lack of a theoretical, normative basis to justify the choice of values. Second, in response to this, the chapter develops a set of values that are informed by the XAI literature and are specifically responsive to the notion of sXAI. Most notably, it focuses on the intrinsic values of self-advocacy, deliberative agency, and reason responsiveness. Third, the chapter demonstrates and assesses the relevance of these values in the context of a VSD exercise. For this exercise, we consider a disobedient robot/AI-system case. Overall, the chapter proposes a VSD framework that integrates intrinsic values tied to sXAI contexts.