It is really too hard to say without knowing your full situation for possible deductibles etc. However, even with the double taxation treaty, most still owe a check to the IRS each year, and for high earners, it goes up more. You could do some strategic tax planning things, pension wise, etc. that could minimise the US side, but it could also make things worse on the swiss side. If you want zero US tax liablitly there is probably little hope other than renouncing citizenship (with some issues here too) or earning less than the foreign earned income/housing exclusions.