There is increasing global interest in market-based climate change policies following the last elections in the United States. In this context an Exxon Mobil chief executive came out in favour of a carbon tax. This paper is concerned with the welfare analysis of Environmental Tax Reforms (ETR), and takes up the claims for the need of an unambiguous and operative definition of the double dividend both for empirical purposes and political advisement. In this paper, we contest the usual definition of the second dividend and its assimilation to an "efficiency dividend". We propose alternative definitions by suggesting a different splitting of the total welfare variation between the first and the second dividend in order to isolate the efficiency effects of the ETR. The new definitions become clearly understandable and easy for economic and policy interpretation. Concepts like "weak" and "strong" double dividend turn out to be unnecessary. Finally, we analyze ETR for the US economy to illustrate the advantages of the proposed definitions for policy implementation.