Sustainability and energy sobriety should guide the "why" and the "how" of 6G. It is mandatory that the 6G infrastructure and services have a very low environmental footprint, but also, and more importantly, the 6G technology should be designed on the 5G basis for enabling added-value services for the society and to mitigate the environment footprint. This paper presents a vision for 6G network as an enabler for a more sustainable society, e.g. by enabling the society of maintenance and care and fostering innovation in the industry. On the other hand, some technology enablers for an energy sober 6G network are presented, along with guidelines for network deployments and for the assessment of the global impact of 6G services.