Josh Chafetz, an associate professor of law at Cornell, is writing a book about congressional power and the separation of powers.

On Wednesday, the House Oversight Committee voted to hold Attorney General Eric H. Holder Jr. in contempt of Congress for refusing to turn over subpoenaed documents relating to Operation Fast and Furious, a program run by the Justice Department’s Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF). The Obama administration appears to be digging in its heels, asserting that the documents are protected by executive privilege. House Speaker John A. Boehner (R-Ohio) has said that unless a deal is reached, the full House will vote on the contempt citation next week.

If the House finds Holder in contempt, what then? Under an 1857 statute, the House can refer the matter to the Justice Department for prosecution in federal court. But the department would almost certainly exercise its prosecutorial discretion and refuse to charge its own leader. Indeed, that happened in 2008, when the House held George W. Bush administration officials Harriet E. Miers and Joshua B. Bolten in contempt for failing to comply with subpoenas related to the 2006 firing of nine U.S. attorneys.

The most likely next step would be for the House to file suit in federal court, seeking a declaratory judgment that Holder is in contempt of Congress and an injunction ordering him to comply with the congressional subpoenas. That is how the House went after Miers and Bolten. But their case illustrates why it would be a mistake for lawmakers to follow the same course now.

For one thing, going to the courts sends the wrong message about Congress’s strength. It would be odd and enfeebling for the House to declare someone in contempt and then go, hat in hand, to a federal district judge and ask her to declare that person in contempt.

Perhaps that kind of public humiliation would be worth it if the House actually got what it wanted in court. But that will not happen, as the Miers and Bolten case shows. Although a trial court ruled in the House’s favor, the legal battle took years. The House did not get any information until after the expiration of the Congress in which the subpoenas had been issued, after the end of the Bush administration, and after the U.S. attorneys controversy had faded from public attention. And if the executive had needed to drag out court proceedings even longer, there is no doubt that it could have, further frustrating the role of Congress in overseeing the executive branch. If this is what winning in the courts looks like, the House should want no part of it.

Fortunately, the House has other options. A better way of dealing with such controversies, a way that is truer to our constitutional traditions and history, requires recognizing that, in such high-level separation-of-powers fights, the line between law and politics breaks down almost entirely. It is precisely in such cases that our constitutional order seeks to harness “ambition . . . to counteract ambition,” to borrow James Madison’s words. Once we view this as a political battle, we can see the panoply of political tools available to Congress.

There are some big guns: If the House holds Holder in contempt, it can send its sergeant-at-arms to arrest him and hold him until his contempt is purged. The House has arrested and held executive-branch officials twice in U.S. history, although the last time was nearly a century ago. And traditionally, courts will inquire into the House’s jurisdiction to arrest — which undoubtedly exists here — but not its reasons for doing so. This option is risky; it even raises the possibility of a standoff between the House sergeant-at-arms and the executive-branch police tasked with protecting Holder. But executive-branch contempt of court also raises the possibility of a standoff between judicial marshals and executive-branch police. Such risks are always attendant in high-stakes separation-of-powers controversies.

The House could also impeach Holder — and there is a good argument to be made that impeachment, which must be tried in the Senate, is the way to go after a Senate-confirmed Cabinet officer. The Democratic Senate may refuse to convict Holder, but simply facing impeachment proceedings is quite punishing — just ask Bill Clinton.

Or consider the House’s power of the purse. It could threaten to cut funding to the ATF in particular or to the Justice Department as a whole. It could even refuse to pay Holder’s salary until he purges his contempt. Lower down the scale of confrontation, the House could pass a resolution censuring him or continue to hold hearings designed to embarrass him.

The House would risk looking petty in doing any of this, just as the Obama administration risks looking petty by withholding information from Congress. As with all high-level separation-of-powers conflicts, whoever can win public opinion will ultimately win the day. And that is as it should be; after all, these people are competing to be our public servants. It is a fundamentally political contest, and it should be settled by political means.