Hang on. If it reduces taxable income, that's not the same as topping up. You were right in the first part where you said it's a tax credit. But those subtract

Hang on. If it reduces taxable income, that's not the same as topping up. You were right in the first part where you said it's a tax credit. But those subtract from your tax owed, not your taxable income, a difference that's important because it's a pretty large sum in dollars. Here's a simplified model to illustrate: Wlog, suppose the US charges a straight m rate per dollar, country X charges n. Suppose first k dollars of an expat are untaxed by the US. Let's say the expat makes j dollars, an equivalent US citizen in the US makes the same, and so too a citizen of X. The citizen of X is taxed nj by X, the US citizen resident in the US is taxed mj, and the expat would be charged (j-k-nj)×m by the US and nj by X for a total of m(j-k-nj) + nj if it were a deduction to taxable income. Notably if there's no fixed deduction, every tax rate causes you to pay more than otherwise.