TRIZ is essentially a distillation of the ‘first principles’ of problem solving. It was originally developed for complicated technical problem and opportunity situations and, through ARIZ, has been deeply optimized for such roles. Increasingly, however, the world has become dominated by complex, non-technical situations, and in these environments many of the tools, methods and processes of traditional TRIZ become highly inappropriate. Complex situations are characterised by an absence of ‘root-causes’, have cause-effect relationships that are frequently tenuous, and are vulnerable to highly non-linear ‘butterfly effects’. The paper describes the creation and verification of coherent non-linear, iterative divergent/convergent processes that take advantage of the first principle nature of TRIZ, and complement them with essential pieces from other domains of science. In a final section, the paper provides change agents with a menu of heuristics for determining the most appropriate TRIZ and non-TRIZ tools and strategies for any given situation.