The international treaty known as the Paris Agreement requires global greenhouse gas emissions to decrease at a pace that will limit global warming to 1.5 degrees Celsius. Given the pressure on all sectors to reduce their emissions to meet this target, the ICT sector must begin to explore how to innovate under constraint for the first time. This could mean facing the unprecedented dilemma of having to choose between innovations, in which case the community will need to develop processes for making collective decisions regarding which innovations are most deserving of their carbon costs. In this paper, we expose tensions in collaboratively prioritising ICT innovation under constraints, and discuss the considerations and approaches the ICT sector may require to make such decisions effectively across the sector. This opens up a new area of research where we envision HCI expertise can inform and resolve such tensions for values-based and target-led ICT innovation towards a sustainable future.