Vaunted as the next frontier within the scope of the Internet of Things (IoT), Edge Computing (EC) is seen as a means to improve efficiency and privacy across IoT infrastructures. This is because it enables data to be processed where it originates, that is, at the so-called ‘edge’ of the network, this being within, or close to, individual Internet-connected devices. Consequently, EC is considered more secure than conventional processing methods as data need not travel over networks to and from the centralised ‘Cloud’. We argue that EC optimisation might also offer credible benefits for environmental sustainability, particularly regarding decarbonisation by minimising data-distribution. To make this case, we outline the creation of two integrated design fictions which highlight environmental harms resulting from widespread Cloud data management, as well as envisioning potential future sustainability advantages of Edge-based processing. Based upon our process, we put forward an initial model for Sustainable Edge Computing.