How to demonstrate a US tax bill of $0?

I think I should have a US tax bill of $0, but am puzzled how use Form 1116 to show this. My affairs are simple and I hope someone can help me. I am fully taxed in the UK on my worldwide income. Every piece of income I have is taxed at a higher rate in the UK that it would be if I lived in the U.S.

I have only a few sources of income: a UK salary, UK bank interest, and some US bank interest and US stock dividends. All are reported to my UK self-assessment. The UK tax charge on each source exceeds the possible US tax charge. (I do not use Form 2555.)

I am seeking the simplest way to show that I have a US tax due of $0. I have read a TurboTax page, which says,

"Resourced by treaty" relates to tax treaties the US has with other countries. You complete a Form 1116 for this category if the country in which you worked has a special agreement with the US about how it taxes your income as a foreigner. Under "resourced by treaty" agreements, all of your income, including any money you made in the U.S., counts as income from the treaty country when figuring out the taxes you owe it".

I am focusing on the words "all of your income". Does this mean that I need not complete a 1116 "general" (for my UK salary) or 1116 "passive" (for my UK bank interest)? Can I simply put everything on a 1116 "resourced by treaty", state my UK tax bill and be done?

Based on the facts presented I am surprised to see that you calculate that you owe exactly $zero; but perhaps you have credits such as child tax credits you are using to offset your US liability?

Well, maybe not a tax bill of $0, but quite close.

I find it weird that by following the instructions for Form 1116 I seem to end up paying so little tax.  What do you think about the following simplified example?

Suppose my total income is $100,000 UK wages and $10,000 US qualified dividends. I am taxed in the UK on my worldwide income. What US tax should I pay? Assume I am single, my deduction is 6100 and exemption 3900.

From the Qualified Dividends Worksheet (or direct computation), my US nominal tax is:

0.28*(100000-6100-3900) - 6706.75 + 0.15*(10000) = 19993.

On Form 1116 General my allowable tax credit for my UK wages is figured as:

19993 * (100000-6100*100000/110000)/(110000-6100-10000*0.6212)
= 19331.

The denominator of (110000-6100-10000*0.6212) is from the adjustment required for line 18 of Form 1116. This adjustment reduces the dividend income to an amount which if taxed at 39.6% would result in the same tax as the full amount taxed at 15% (a helpful fact to understand, but which the 1116 instructions do not explain. One is left to guess at where the multiplier 0.6212 (=1-0.15/0.396) comes from. But I digress ..  )

Assume I can take all this as foreign tax credit since my UK tax bill on my wages exceeds 19331.

This leaves me paying the US only $632. Whereas under tax treaty, the US has the right to take 15% of dividend income, which would be $1500.  

Is that right or wrong?

When I come to complete my UK taxes, where I am charged 32.5% on dividends, with a notional 10% credit, do I take a credit for tax paid to the US on these dividends of just $632?

I.e. the UK should get

(10/9)*10000*(.325) - 632 - (10/9)10000*(1/10)=$1867 for the dividends

plus the tax on my wages.

p.s. Note that it is only if I were paying US tax at the marginal rate of 39.6% that I would end up paying the US $1500 on the dividends. Also, Form 1116 is written as if the reader prefers to take an adjustment exception, but may do so only under certain conditions. But that is not so. The tax credit will be greater by *not* taking the adjustment exception, unless we are talking about a rather wealthy person who is paying tax at 39.6% and whose dividend income is greater than her wages.