In society in general and within computing in particular, there has, and continues to be, a focus on faster, cheaper, better etc. Such perspectives clash with the fact that impeding climate change and the need for radically decreased CO2 emissions (c.f. the Paris Agreement) will have fundamental and far-reaching ramification for computing and for all other sectors of society during the coming decades. In the call for the first Computing within Limits workshop, it was stated that "A goal of this community is to impact society through the design and development of computing systems in the abundant present for use in a future of limits and/or scarcity."There have since been several contributions to Computing within Limits that have accepted the challenge of discussing and imagining what such systems as well as what "a future of limits and/or scarcity"could look like. Despite this, there is currently no consensus about what exactly such a future entails and the community can consequently only offer hazy ideas about exactly what systems we should strive to design and develop. The basic problem can be summed up as follows: we know that fundamental changes are necessary and will come, but we still struggle with envisioning what a post-growth/decarbonising society looks like and what computing systems need to be designed and developed for use in such futures, or, to support that transition. In this paper we argue that the work of imagining an actionable "future of limits"could benefit from using the "carbon law"as a starting point. The carbon law is based on work in the environmental sciences and we exemplify how it can be used to generate requirements that can guide the development of computing systems for a future of limits. While these lessons are general, we exemplify by describing a research project that aims to support the KTH Royal Institute of Technology's goal of-in line with the carbon law-radically reducing CO2 emissions from academic flying over the next decade. We give examples of how computing can aid in this task, including by presenting visualisation tools that we have developed to support the KTH carbon abatement goals. We also discuss the role of computer science in general and of Computing within Limits in particular in supporting the transition to a more sustainable (or at least a less unsustainable) future.