Sustainability in and through digital technology has up until very recently been framed in modernist terms, focused on quantification and optimization of resource use. This framing has been frequently criticized for being limited in scope and impact, and has been framed as shallow sustainability in environmental ethics literature. Sustainability within computational creativity (CC) research is an emerging topic. To avoid the pitfalls of shallow sustainability, we conceptualise and propose a ’deep sustainability’ perspective in computational creativity research. This enables a relational approach to the predicament of the climate crisis by critically examining the values and assumptions that underpin CC research. Building on this, we reflect on and discuss what deep sustain-ability would mean for the future of sustainability research within the CC community, and raise critical questions with the particular aim of sparking discussions around how sustainability research is and ought to be approached within the community.