Low effective tax rates make it more affordable for Paris Hilton to travel to Cannes. Valery Hache/AFP

One of the cornerstones of American income tax policy is that taxes are progressive. People who make more money devote a higher share of their income to federal income taxes than people who make less money. That allows for a redistribution of wealth that lowers inequality.

That's how it's supposed to work, at least.

But new data out this spring from the IRS gives us a closer look of how the income tax works at the pinnacle of the income distribution -- not just the top 1 percent, or even the top 0.1 percent, but among the rarified realm of the 0.01 and even the 0.001 percent. Those latter two categories are new in the IRS report this year, reflecting a growing public interest in the ultra-wealthy and their effects on the economy.

The IRS found that as you go from being merely wealthy (the 1 percent) to super-duper wealthy (the 0.001 percent), your average federal income tax rate actually goes down. In other words, the progressivity of the federal income tax starts to fall apart at the upper reaches of the income distribution. Take a look.

The average tax paid across the top half of American society by income -- the top 50 percent of earners -- was 14.33 percent in 2012, according to the IRS. Climbing up the income ladder the tax rate increases to 22.83 percent for the top 1 percent of earners.

But when you start to slice that group further -- all the way up to the top 0.001 percent -- you'll notice that the effective tax rate falls steadily to 17.60 percent at the very top.

In other words, a person in the top 0.001 percent income bracket -- who would have an adjusted gross income of at least $62,000,000 -- pays the nearly same effective tax rate as somebody in the top 20 percent bracket who makes $85,000 in adjusted gross income.

That's not how federal income taxes were, at least originally, designed to work. The super-rich pay a relatively low rate for a variety of reasons. They benefit from a whole host of deductions -- like the mortgage on a yacht, for instance -- and other tax benefits that many people don't qualify for.

Chief among these is the lower tax rate on capital gains -- think investment income. That maxes out at about 24 percent when you factor in a Medicare surtax that applies to some investment income. But wages are taxed at a top rate of 39.6 percent. Since many of the super-rich get most of their earnings from investments, they disproportionately reap the benefits of that lower capital gains tax rate.

In the year this data was compiled, 2012, the top capital gains rate was lower still, at 15 percent. So it will be interesting to see whether the recent capital gains rate hike -- up to a maximum of 24 percent -- has much of an impact on these trends.

Some politicians, most notably Bernie Sanders, have called for higher tax rates on the super-rich. Sanders would like to see the top income tax rate rise to 90 percent, where it was back in the 1940s and 1950s.

But the numbers above suggest that simply ratcheting up the income tax and ignoring capital gains won't take a huge bite out of inequality, particularly not among the super-rich. If policymakers wanted to really take more from the ultra-rich, they would tax investment income much more progressively.

This post was updated to clarify that the top capital gains tax rate in 2012 was 15 percent.