The traditional view that excise taxes are regressive has been challenged. I document the history of the term regressive tax, show that traditional definitions have always found cigarette taxes to be regressive, and illustrate the implications of the greater price responsiveness observed among the poor. I explain the different definitions of tax burden: accounting, welfare-based willingness to pay, and welfare-based time inconsistent. Progressivity (equity across income groups) is sensitive to the way in which tax burden is assessed. Analysis of horizontal equity (fairness within a given income group) shows that cigarette taxes heavily burden poor smokers who do not quit, no matter how tax burden is assessed.