The residents of six US states (Alabama, Iowa, Louisiana, Missouri, Montana, and Oregon) get to exclude or deduct all or part of their federal income taxes paid when they calculate their taxable income for state income tax purposes. Critics have called this deduction “costly and regressive.” The critics are probably right, but not for the reasons they think. The critics of the deduction overlook the fact that the states that allow deductibility of federal income tax for state tax purposes use a different state income “tax base” or “scale” than other states. Most state income tax regimes use a tax base that includes federal income taxes paid (we call it FTI), but the six states listed above use an income tax base that excludes federal income taxes (the FTE base). The two tax bases can translated from one to the other. Indeed, this paper provides original formulae for converting the FTE base into its FTI equivalent and vice verce. Because of this equivalence, one state income tax base is not a priori better than another. But when we convert FTE income tax bases into their FTI equivalents, we find a pervasive trend. States with FTE income tax regimes systematically have more regressive income tax regimes than states with FTI bases. We argue that taxpayers and legislators under-adjust relative to our translation formula when comparing FTE regimes to FTI regimes, causing the systematic regressive trend in states with FTE regimes.