A terrific story the other day by Jesse Drucker at Bloomberg got me thinking: Would it really matter very much if the U.S. cut its corporate tax rate from the current 35 percent to 25 percent? While that idea has growing support in Congress, it may be a classic case of closing the barn door long after the horse has escaped. It may be that only a fundamental change in the way we tax multi-national companies, and not just a cut in rates, can fix the many problems that vex our corporate tax system.

Jesse took a deep dive into the tax status of Google Inc. and found that thanks to some clever—but apparently perfectly legal—planning, Google cut its taxes by more than $3 billion over the past three years and drove its overseas tax rate to 2.4 percent. Jesse figured Google boosted after-tax earnings by 26 percent last year alone with just some clever tax tricks.

Read the story for all the gory details, but essentially, Google’s strategy relies on its ability to shift intellectual property, such as the rights to its search technology, to foreign subsidiaries that reside in low-tax countries. The game is simple: Shift as many costs as possible to a high-tax jurisdiction such as the U.S. and move as much income as possible to a low-tax country such as Ireland. That’s exactly what Google did. In fact, to maximize its tax savings, Google shuffled its income to Ireland, then to shell companies in Bermuda and then to another shell in the Netherlands and finally back to Bermuda. Once Google’s income completed the tax equivalent of the Grand Tour, its tax liability on foreign income was roughly nothing. And Goggle is hardly the only company doing this.

In theory, for the purpose of calculating U.S. tax, Google’s Irish subsidy is supposed to pay the same price for technology as an unrelated company would. The Internal Revenue Service struggles to calculate this “transfer pricing” when it applies to an auto bumper. It is overwhelmed when it must do the same for intangibles such as search technology, software, or drug patents. Just think about it: What would Google charge Yahoo for the rights to its technology? A gazillion dollars? Two gazillion? The result is open-season on the Tax Code. And that (along with the large number of businesses that don’t file as corporations) explains why, despite having among the highest statutory corporate rates in the world, the tax generates relatively little revenue.

President Obama wants to raise more by cracking down on some egregious overseas tax gimmicks. But let’s face it, the IRS will never catch up with these constantly evolving strategies. And even more than a rate cut, these enforcement efforts only dodge fundamental problem.

In part, we still have a tax system that was designed for factory-heavy manufacturers. But we have an economy whose value increasingly lies with human capital-based companies such as Google. It is not so easy for a company to move a factory (though, of course, hardly impossible). But moving licenses or financial assets can be done with the click of a mouse. And if all it takes is that mouse and a couple of sharp lawyers to drive a company’s tax rate to effectively nothing, merely cutting the U.S. corporate rate to 25 percent won’t accomplish very much.

The real problem may be the fundamental structure of the U.S. corporate tax system. The U.S. attempts to tax worldwide income while giving companies a credit for taxes they pay to those countries where they earn foreign income. Many other industrialized companies instead use a territorial system, which taxes only income earned at home. Others use a hybrid.

It is time to think way outside of the box. There are plenty of options for dramatic reform. We could cut the corporate rate below even 25 percent but also require multinationals to pay tax immediately rather than letting them defer their liability for years as they do today. We could follow the rest of the world and consider some form of territorial system. We could repeal the corporate tax entirely and enact a Value-Added Tax. None of these is perfect, but each has advantages over the current mess.

I am not suggesting that lowering the corporate rate while dumping as many targeted corporate tax subsidies as possible is a bad idea. In may, in fact, be the best we can do. But when lawmakers tell you how a modest rate reduction will make U.S. firms more competitive, keep Jesse’s story in mind. If you don’t believe me, just Google it.

Tax experts will argue about nearly anything. But on one issue, there is something approaching a consensus: Corporate tax rates in the U.S. are too high. Where all that harmony turns dissonant, however, is over the matter of what to do about it. Cutting the corporate rate, it turns out, raises all sorts of complex technical problems, to say nothing of being a political nightmare.