When you start receiving pension distributions, your monthly benefit will have both a taxable and non-taxable portion. The central non-taxable portion comprises all your contributions that have not been deducted from taxable income in the U.S. The non-taxable amount also includes employer contributions reported on your U.S. tax return. Altogether, this will constitute your pension "cost."
The taxable portion will be calculated using an IRS calculator, which factors in your pension cost and age when you receive the benefits. This is not a simple calculation, but once it's done the first time, it will be easier to calculate in the following years.
Depending on the nature of their tax treaties, some countries have a far more straightforward way of calculating the taxable portion. i.e., 25% of U.K. income is non-taxable in the U.S.
Each Tax Treaty has a "Saving Clause." Paragraph 4 of Article 1 of the U.K./U.S. Convention reads:
Notwithstanding any provision of this Convention except paragraph 5 of this Article, a Contracting State may tax its residents (as determined under Article 4 (Residence)) and, because of citizenship, may tax its citizens, as if this Convention had not come into effect.
In effect, the Saving Clause states that most tax exemptions apply only to non-residents (i.e., U.K. citizens are required to file U.S. non-resident tax returns because they receive income from U.S. sources). Paragraph 5 lists limited types of income where the exemption applies to U.S. citizens.
There are only two means of tax reduction available to U.S. citizens paying foreign taxes:
The foreign-earned income exclusion.
The foreign tax credit (which offers relief from double taxation).