This paper clarifies some conceptual shortcomings of the empirical environmental Kuznets curve (EKC) literature that arise because of the hitherto inadequate application of unit root and cointegration techniques. The literature to date has ignored the fact, and a fortiori the consequences, that powers of integrated processes are themselves not integrated processes. The paper explains why standard methods should not be applied and discusses some recently proposed viable estimation and testing approaches for cointegrating polynomial regressions. The application to CO₂ and SO₂ emissions data shows that using appropriate methods leads to strongly reduced evidence for a cointegrating EKC compared to typical but conceptually not sound findings.