U.S. federal regulations impose nearly $2 trillion in annual costs on American business, according to the Small Business Administration. President Barack Obama thinks that’s probably too much and now wants regulators to strike out needless red tape. Better late than never. Even better, Congress should have more power to do the cleanup itself.

At the very least, Obama’s executive order is another hint to corporate America that the president is eager to mend fences after a fractious 2010. And no doubt business groups will applaud, just as they did last month’s deal on tax rates and Obama’s reconstitution of much of President Bill Clinton’s economic team. Congressional Republicans are likely to approve as well, though some may grumble that the initiative should have preceded last year’s regulatory overhauls of Wall Street and the healthcare industry.

Yet Obama’s timing actually matches up with the onslaught of rule-writing stemming from those reform bills. Financial regulators, for instance, may spend two years or more adding meat to the bones of the Dodd-Frank law that was intended to prevent a repeat of the banking crisis. The president’s move is a reminder to keep an eye on the costs of old rules as well as new ones, even though the directive is more geared toward the former than the latter.

But here is the problem: Expecting regulators to whittle down their own responsibilities much is incredibly optimistic. They are hired to regulate, and broadly speaking the more they perform that function, the more funding and influence come their way. So there’s a case for giving lawmakers greater ability to make changes if regulators can’t bring themselves to do it — presidential order or not.

One idea is a bill introduced last year, and likely to be resubmitted, that would require Congress and the president to sign off on any new rule proposed by federal agencies that would have an annual economic impact of $100 million or more. Some 80 or more rules a year might qualify for such a review. Though it might not always make perfect sense, there’s also some merit behind efforts to force regulators to eliminate one old rule with similar cost for each new one they wish to impose. Initiatives like these would help ensure the ever-encroaching regulatory tangle was regularly pruned.