Super PACs — groups that can accept unlimited contributions and spend unlimited amounts to support or oppose candidates — are the Kim Kardashians of the campaign finance world, soaking up more than their share of media attention. In contrast, their less flashy counterparts — such as movie studio executives — arguably are bigger political players, but they receive dramatically less coverage.

These groups, referred to by the applicable sections of the tax code as 501(c)(4) and 501(c)(6) organizations, were pumping money into federal campaigns even before the Supreme Court’s Citizens United decision, but they have increased their spending dramatically during the past two years. In the last election cycle, groups such as Crossroads GPS, the American Action Network and the U.S. Chamber of Commerce spent more than $135 million and are certain to spend much, much more this year.

Tax law permits groups such as these — purportedly created to promote social welfare or as business leagues — to participate in political campaigns yet allows them to keep the identities of their funders secret.

So who is funding these groups? Until recently, it had been nearly impossible to confirm significant corporate involvement. Earlier this month, Citizens for Responsibility and Ethics in Washington discovered that insurance giant Aetna donated more than $3 million to AAN and more than $4.4 million to the U.S. Chamber of Commerce in 2011.

Ironically, Aetna Chairman Mark T. Bertolini recently spoke out against a shareholder proposal to require greater disclosure of the company’s political spending, arguing that he was in favor of transparency and accountability but that a new rule was “unwarranted.” When confronted about Aetna’s secret political contributions, Bertolini claimed they were made to support “educational activities.” This is true only if you believe vicious, deceptive television attack ads are educational. It is naive to think other companies aren’t making similar contributions.

Why is this bad?

First, Aetna is using Americans’ insurance premiums to secretly influence our votes. Voters should know who is behind political ads so they can put them in the proper context.

Second, just because we don’t know who is paying to help defeat a particular candidate doesn’t mean everyone is in the dark. Aetna and its donating corporate counterparts likely ensure the candidates benefiting from all of this largess are aware — and suitably grateful — for the assistance. And if elected officials then use their positions to carry their corporate benefactors’ water, who will know?

There is a simple solution to all of this secret political campaign spending by tax-exempt groups: ban it.

Under current law, engaging in political activity cannot be the primary purpose of these groups. While the IRS has been silent as to the exact definition of “primary purpose,” it generally has been assumed to mean groups must spend less than 50 percent of their budgets on political activities. Why not change the law to prohibit tax-exempt groups from participating in political campaigns at all?

Tax-exempt organizations would still be permitted to engage in as much lobbying, education and grass-roots activity as they want, but a ban would draw a clear line between political and policy-related activities. If organizations or their funders want to participate in political activity, they could do so through separate political organizations: super PACs, which must disclose their donors and expenditures.

Banning political activity by tax-exempt groups likely would not run afoul of the First Amendment. Upholding an analogous ban on lobbying activity — also protected by the First Amendment — by charities in 1983, the Supreme Court said Congress could choose not to subsidize lobbying. The court noted that charities could establish separate but related groups to lobby, just as tax-exempt organizations could set up separate political groups under a ban. In fact, it was just this sort of lobbying activity for which 501(c)(4) organizations were created in the first place.

The law needs to be changed to require the disclosure supported by the Supreme Court and expected by the public. Corporations as well as millionaires and billionaires seeking to influence American elections can no longer be permitted to manipulate tax law to hide their activities from public view. Let’s see whether they relish the spotlight as much as Ms. Kardashian.

Melanie Sloan is executive director of Citizens for Responsibility and Ethics in Washington.