“The only way that any current ethics rules or future ethics rules will work is if there’s a way to enforce these rules and a way for the Supreme Court justices to understand how they apply,” he said. “So, therefore you need an internal body that can provide the ethics expert advice and also gather facts in the circumstances where there are potential violations that need to be resolved.”

But enforcement is the rub. A recurring theme in the hearing and the broader discussion of potential change was the lack of an obvious remedy if a justice flouted a rule or contended that it was inapplicable to something he or she wanted to do.

“What is the enforcement mechanism?” Thomas Dupree, a partner at Gibson, Dunn and Crutcher, asked at the hearing. Raising a constitutional impossibility for rhetorical effect, he added: “Is there going to be some superior tribunal to the Supreme Court that is going to disqualify the justices?”

For the same reason, it is far from clear that Chief Justice Roberts could unilaterally impose an ethics code on the rest of the court, even if he were more inclined to do so than he appears to be. If another justice chose to ignore any edict, the chief justice would have no obvious way to enforce it.

The proposals that have been floated carry drawbacks. One is to have the rest of the court sit in judgment of a ninth who is accused of some transgressions, but the justices are likely to reject such a role for collegiality reasons given the guarantee of lifetime tenure and the size of the court. Another is to have a panel of appeals court judges pass judgment on a justice, but that raises structural problems since they are subordinate judges.

Indeed, it is hard to envision any binding way to enforce a code of ethics on the Supreme Court. But Mr. Gillers said there would still be value in the court adopting one, predicting that justices would be inclined to comply with a standard they took an oath to obey as a matter of honor and to avoid criticism.

“If the court voluntarily adopted an ethics code, academics, the media and court watchers could call out transgressions or failures to recuse,” he said. “The very act of acknowledging ‘I am bound by this’ would give the public confidence that they will behave honorably, because violation carries a badge of shame.”