In response to a growing popular concern for `sustainability', Green Computing has emerged as a new `sustainability' discourse in which researchers explore solutions to reduce the environmental impact of computing technologies themselves, as well as solutions to reduce the environmental impact of other activities and behaviours through the development of new technologies. Despite good intentions and enthusiasm for the cause, there is little evidence of Green Computing having had significant or long-term impacts, and indeed, as one potential indicator, even combined with all of the efforts of many other disciplines, the exponential curve of growth in carbon emissions continues unabated. This dissertation aims to understand the reasons why Green Computing may have had a limited impact to date, and explore alternative approaches to `sustainability' that may enable greater impact by computing. To begin, key assumptions underpinning Green Computing discourse are exposed in order to contextualise it within the broader debate surrounding an agenda for `sustainability' -- the term itself, while gaining significant traction in popular culture, is deeply contested. It is shown that the discursive characteristics of Green Computing, along with its specific appropriation of the term `sustainability', reinforce a set of values that ultimately undermine its solutions and limit its impact. An alternative discourse is proposed that avoids reinforcement of problematic values, and a radically different conception of `sustainability', and the role that computing may play in contributing to a `sustainable' future, is proposed in a new discourse, namely Cyber-Sustainability. To illustrate the difference in solutions that might emerge from Cyber-Sustainability, an initial set of propositional solutions are presented in the form of patterns, which are offered here as an invitation for others to join in the further elaboration of these patterns towards a comprehensive pattern language.