Robert S. Mueller III. (Mark Wilson/Getty Images)

IT SEEMS unthinkable, but Washington has been abuzz with rumors that President Trump might fire special counsel Robert S. Mueller III, the man investigating Russia’s election-year hacking and any possible Trump campaign collusion. We have viewed much of the talk to date about impeachment as overheated. But firing Mr. Mueller would, more than anything else the president has done in office, firm up a case that Mr. Trump is obstructing justice.

In a Tuesday Senate hearing, Deputy Attorney General Rod J. Rosenstein, who could be called on to perform the firing, did not promise not to. But he set a high bar, committing that “I’m not going to follow any orders unless I believe those are lawful and appropriate orders.”

On Mr. Rosenstein’s first standard — legality — there is an argument that Mr. Trump would have the authority to dismiss Mr. Mueller, though doing so would not be simple. On appropriateness, however, there is no question.

Conservative commentators, including two with ties to Mr. Trump, have mentioned the possibility of dismissing Mr. Mueller or have begun making the case for doing so. Though the special counsel has a sterling reputation and broad bipartisan support, one charge is that he is friends with former FBI director James B. Comey, whom Mr. Trump unceremoniously sacked, which could color his views on the president and his circle. Another apparent concern is that Mr. Mueller hired staff who donated money to Democrats in the past.

We do not dismiss the concerns. Given the stakes, it is incumbent on Mr. Mueller to live up to his reputation and run a spotless investigation. He may, for example, insulate as much as possible any obstruction-of-justice probe from anyone who could be open to any kind of partisan attack.

But on the big picture, House Speaker Paul D. Ryan (R-Wis.) got it right on Tuesday. “I know Bob Mueller,” Mr. Ryan said. “I have confidence in Bob Mueller.” Mr. Mueller’s track record is that of a longtime public servant, appointed to high positions by Republican and Democratic presidents and so well-respected that his 10-year term as FBI director was extended for an extra two years on a unanimous Senate vote. The relatively minor concerns expressed about him do not suggest he is incapable of acquitting himself with the same professionalism he has shown over the course of decades. On the other hand, according to strong testimony from Mr. Comey, the president has already tried to improperly influence the very investigation that some are insinuating, with no evidence, Mr. Mueller might tilt.

Firing Mr. Mueller would have to be seen by Congress as part of a concerted and continuing effort to foil a serious investigation into Mr. Trump and his associates. To start, lawmakers would have to reinstate a special counsel by acclamation. And that would be only the first step.