Environmental Kuznets curve (EKC) analysis links changes in environmental quality to national economic growth. The reduced form models, however, do not provide insight into the underlying processes that generate these changes. We compare EKC models to structural transition models of per capita CO2 emissions and per capita GDP, and find that, for the 16 countries which have undergone such a transition, the initiation of the transition correlates not with income levels but with historic events related to the oil price shocks of the 1970s and the policies that followed them. In contrast to previous EKC studies of CO2 the transition away from positive emissions elasticities for these 16 countries is found to occur as a sudden, discontinuous transition rather than as a gradual change. We also demonstrate that the third order polynomial 'N' dependence of emissions on income is the result of data aggregation. We conclude that neither the 'U'- nor the 'N'-shaped relationship between CO2 emissions and income provide a reliable indication of future behaviour.