This paper deals with the welfare analysis of green tax reforms. The aims of this paper are to highlight misinterpretations of policy assessments in the double dividend literature, to specify which of the efficiency costs and benefits should be ascribed to each dividend, and then, to propose a definition for the first dividend and the second dividend. We found the Pigou's dividend more appropriate for policy guidance, in contrast to the Ramsey's dividend usually found in mainstream literature. Therefore, we take up some authors' recent claims about the need of unambiguous and operative definitions of these dividends both for empirical purposes, and political advice. Finally, the paper analyzes a green tax reform for the US economy to illustrate the advantages of our definitions for policy assessment. The new definitions proposed in this paper i) overcome some shortcoming of the mainstream current definitions in the literature regarding overestimation of the efficiency costs; and, ii) provide information by themselves and not as a partial view of the whole picture.