Retirement tax questions

I too am confused. Article 18 provides that the pensions or annuities will be taxed in the recipients Contracting nation state. Therefore in my case I have a company pension from the U.K. and my wife and I each receive a state pension, all of which is taxable in the U.S as we are resident in the U.S and citizens. The purpose of the treaty is to avoid double taxation, not any taxation! That would be nice! The pensions are not exempt from U.K. tax so they become subject to U.S. tax for a U.S. resident as I read it.