Green Information Systems (Green IS) provides a socio-technical perspective on the diverse complex phenomena of organisational sustainability. The Cynefin sense-making framework is eminently suitable for making sense of dynamic, complex phenomena and for guiding sensible decisions on how to meet the challenges they present. The Cynefin framework is described here and illustrated in terms of both ordered and unordered business processes. It is the unordered that are the least understood; but they are the most critical when it comes to sustainability. While order may be appropriate in the short term, sustainability issues also demand a more challenging long-term perspective. Just how rapidly and unpredictably business processes can change is well known in the field of IS which understands the revolutionary nature of new digital technologies. This chapter explores ways to manage sustainably in the face of such uncertainty through an appreciation of unordered complexity.