We investigate Carbon Kuznets Curves (CKC) relationships for advanced countries grouped in policy relevant groups - North America and Oceania, South Europe, North Europe - by means of various homogeneous, heterogeneous and shrinkage/Bayesian panel estimators. We try to provide an answer to the question 'how sensitive are the CKC estimates to changes in the level of parameters' heterogeneity?'. We do find that in coherence with their 'policy and economic' commitment to carbon reductions and environmental market-based instruments implementation, bell shapes are present only for northern EU, which leads the group of advanced countries. The other two lag behind. We show for the first time that CKC shapes are present if we net out Europe of the southern and less developed countries. This is coherent with the Kuznets paradigm. The negative side of the tale is that they characterize a bunch of few countries. Other advanced countries lag behind and are far from reaching a CKC dynamics. Heterogeneous and Bayesian estimators clearly show this, with the EU presenting turning points closely around 13 000 per capita Gross Domestic Product (GDP). Heterogeneous panel estimates also show that for lagging countries presumed bell shapes turn into linear relationships. The stability of outcomes across models is stronger when we compare heterogeneous rather than homogeneous models. If it is compared with other studies, our analysis highlights a relative lower variability across specifications.