Justice Thomas once again declined to recuse himself from a case regarding Arizona GOP Chairwoman Kelli Ward’s alleged efforts to set aside the 2020 presidential vote in her state. He was one of two justices who dissented from the court’s decision allowing the Jan. 6 committee to access some of Ms. Ward’s phone records.

Washington is populated by countless power couples, and conflicts of interest—or appearances of them—are bound to occur from time to time. But Ms. Thomas’s activities stand out as particularly blatant. “Ginni Thomas has held so many leadership or advisory positions at conservative pressure groups that it’s hard to keep track of them,” the New Yorker’s Jane Mayer wrote earlier this year. “And many, if not all, of these groups have been involved in cases that have come before her husband.” One glaring example: Ms. Thomas’s consultancy received more than $200,000 from right-wing activist Frank Gaffney’s Center for Security Policy, according to Ms. Mayer, as Mr. Gaffney urged the court to rule favorably on President Donald Trump’s Muslim ban. Justice Thomas voted to uphold the ban, and he did not disclose the $200,000 payment to his wife.

Meanwhile, the Times reported Saturday that a former antiabortion activist, the Rev. Rob Schenck, claims that he was told how the court would rule on a major 2014 birth control case, saying that Justice Samuel A. Alito Jr. tipped off two associates of his. There is limited corroborating evidence, and Justice Alito and others allegedly involved deny this happened. Yet Mr. Schenck’s contemporaneous emails and conversations indicating that he knew the case’s outcome and the author of the opinion are reason to worry. He says he ran “Operation Higher Court,” a years-long effort among conservative activists to ingratiate themselves with justices via donations to the Supreme Court Historical Society, meals and trips to places such as Jackson Hole, Wyoming. “I saw us as pushing the boundaries of appropriateness,” Mr. Schenck said, and the Times’s reporting suggests his operatives achieved high levels of access to certain justices.

An ethics code binds lower-court judges but not Supreme Court justices. Chief Justice Roberts says that justices refer to the code but make their own ethical calls. This is not enough. The justices should formally bind themselves to a judicial code of conduct, rather than simply consulting one when they are so inclined.

Then there is the question of how to enforce such rules. One option is to have the whole court review requests that, for example, certain justices recuse themselves. Another is to create a panel of outside judges, perhaps distinguished retired jurists whose work the high court no longer oversees, to consider Supreme Court ethical questions referred to them.

Critics of such an arrangement point out that, unlike on lower courts, the Supreme Court risks deadlocking 4-4 on major cases if a justice is recused. This could leave important legal questions unresolved and lower courts without definitive precedents to apply. Limiting justices’ work because of their spouses’ conduct, meanwhile, raises the prospect that talented people with professionally active partners will not pursue careers on the bench.

Yet the court’s reputation is indispensable; its power rests both on its constitutional mandate and its credibility. The justices should not continue to dismiss Americans’ declining confidence as the product of misunderstandings about how they work. Moreover, if the court fails to adjust, Congress might step in. Federal lawmakers are considering several reforms, including imposing restrictions on compensated travel and setting requirements that justices must disclose with whom they meet.

Congressional action, however, would no doubt raise separation-of-powers issues. That is all the more reason that justices should acknowledge that they have given the public reason for its mistrust, and take it upon themselves to restore faith in their impartiality.

The Washington Post Editorial Board published this opinion piece on Nov. 26.