This paper describes and compares notions of <i>luxury</i> and <i>new luxury</i> as a social notion of sustainability. The context of the discourse is sustainable interaction design (SID), defined in the paper and attributed to several sources. Several research questions are posed concerning the relationship between luxury, new luxury, quality, and equality in the context of SID. We propose an informal design critical framework that embeds interaction design in terms of luxury and sustainability. Several examples of products and services are analyzed in the proposed framework according to three themes: communications, computer software, and music. The paper concludes by reflecting on the research questions with respect to the framework.