The House Oversight Committee voted Wednesday to hold Attorney General Eric Holder in contempt of Congress for refusing to turn over subpoenaed documents relating to Operation Fast and Furious. 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, it 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. That’s what happened in 2008, when the House held George W. Bush administration officials Harriet Miers and Joshua 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 it would be a mistake for lawmakers to again follow that course.

For one thing, going to the courts sends the wrong message about Congress’s strength. It would be 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 against Miers and Bolten took years. The House did not get any information until after the expiration of the Congress in which the subpoenas had been issued. The Bush administration was out of office, and the U.S. attorneys controversy had faded from public attention. And the executive could have dragged out court proceedings even longer, further frustrating Congress’s oversight role. If this is what winning in the courts looks like, the House should want no part of it.

Fortunately, it has other options. A better way of dealing with such controversies, one truer to our constitutional traditions and history, requires recognizing that, in 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,” as James Madison put it. 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. 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.

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 the House could use its power of the purse. It could threaten to cut funding to the bureau running the Fast and Furious program 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 risks 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 conflicts over the separation of powers, 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 should be settled by political means.

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