In this paper we focus on the design, development, and responsible use of the flagship technology of Industry 4.0, namely the digital twin (DT). After a brief review of the literature on industrial applications of the digital twin in a smart manufacturing environment, we look at usual misconceptions about this emerging concept, which often hinder the democratization of the digital twin or pushes to put too many resources at stake compared to the needs. Therefore, we propose to integrate lean data and digital sobriety at the design phase of the DT through a generic architecture including dynamic accuracy management. We pre-sent here the principle of our approach, an application example, as well as some adjustment capabilities.