THE CONSTITUTION says that federal judges “shall hold their Offices during good Behaviour” — for life, that is, unless they commit an impeachable offense. Which brings us to the allegations of domestic violence against Mark E. Fuller, a U.S. District Court judge in Montgomery, Ala.

On Aug. 9, first responders in Atlanta received a call from a woman who said her husband was “beating on me” in a hotel room. At the scene, they found the judge’s wife, Kelli Fuller, with cuts on her mouth and forehead. Ms. Fuller said she had accused her husband of an extramarital affair, whereupon he threw her to the ground, pulled her by the hair, kicked her and hit her in the face. The judge’s story was that Ms. Fuller threw a glass at him, after which he defensively grabbed her hair and threw her off him but didn’t strike her.

Atlanta police arrested and jailed Judge Fuller on charges of misdemeanor battery; he posted $5,000 bail and eventually submitted to a pretrial diversion program. If he completes 24 weekly counseling sessions, all charges will be dismissed — a common outcome in first-offender domestic abuse cases. It’s similar to the bargain Baltimore Ravens star Ray Rice struck with prosecutors in New Jersey — before a leaked videotape of his assault on Janay Palmer cost him his job.

As with the Rice deal, Judge Fuller’s plea agreement means there will be no trial to establish the facts. In Mr. Rice’s case, the blanks got filled in by a leaked video. In Judge Fuller’s case, the U.S. Court of Appeals for the 11th Circuit has started an investigation, pursuant to a federal judicial ethics law, which could lead to a reprimand or, at most, a recommendation that he be referred to Congress for impeachment.

It’s all very roundabout — indeed, much too slow for many Alabama elected officials; politicians from both parties have called for Judge Fuller’s resignation, including the state’s two Republican U.S. senators, who had supported his appointment by President George W. Bush in 2002. Judge Fuller said he “deeply regret[s] this incident” but refuses to step down. Meanwhile, he is effectively suspended from hearing cases, pending the 11th Circuit investigation.

The members of Congress calling for the judge’s resignation say they want to demonstrate that there is no excuse for domestic violence and that it is doubly repugnant when allegedly committed by someone who is sworn to dispense justice. That’s true, but with their impeachment powers, these politicians could investigate and punish Judge Fuller themselves, starting tomorrow, if they were so inclined.

As we read the history, impeachment for off-the-bench misconduct by a federal judge is rare; impeachment for domestic violence would be unprecedented. However, it belongs on the list of offenses potentially serious enough to warrant disqualification from “any Office of honor, Trust, or Profit under the United States”; certainly it fits no reasonable definition of “good Behaviour.” Presiding over a federal court, unlike football, is not a game. If the facts of Judge Fuller’s case warrant it, Congress should not hesitate to proceed against him.