In this article, we aim to strengthen the basis of designing for values, by relating it to philosophy of technology. We start by discussing several theories to understand technology-induced value mediation: mediation approach, technology assessment methods, and types of value change. We continue by connecting these theories to design practice by proposing a new design for values methodology: Values that Matter. This methodology provides the means to evaluate moral mediation of technology during the design process and to responsibly design for it. The methodology is explained by the redesign of continuous vital sign monitoring technology in hospitalized patients.