But this narrow view of the president’s options rests on a misunderstanding of basic constitutional principles. Ever since the founding, presidents, Congresses and the Supreme Court have recognized that the chief executive has constitutional power to remove executive officers. As James Madison noted in 1789: “Is the power of displacing an executive power? I conceive that if any power whatsoever is in its nature executive, it is the power of appointing, overseeing, and controlling those who execute the laws.” In Myers v. U.S. (1926), the Supreme Court observed “it was natural, therefore, for those who framed our Constitution to regard the words ‘executive power’ as including” the power to remove executive officers.

A regulation issued by the Justice Department should not be read to limit the president’s constitutional power to remove officers. Otherwise, a mere cabinet officer could prevent future presidents from exercising the constitutional authorities of their office. The chief executive commands the attorney general, not the other way around.

A bipartisan group of senators are currently mulling a proposal to prevent the president from firing Mr. Mueller except for cause, and to allow the courts to review his removal. The Senate Judiciary Committee has scheduled the bill for a possible vote next week.

But any law that prevents the president from removing executive officers would be constitutionally problematic. In his lonely dissent in Morrison v. Olson (1988), Justice Antonin Scalia noted that independent counsels would become unhinged Inspector Javerts. “Frequently an issue of this sort will come before the Court clad, so to speak, in sheep’s clothing,” Mr. Scalia wrote. “But this wolf comes as a wolf.”

Mr. Scalia had in mind the Iran-contra investigation, which attempted to criminalize a separation of powers dispute between the executive and legislative branches over foreign policy. In the following decade, Democrats belatedly saw the light, too. Ken Starr’s investigation of Bill Clinton lasted for years, consumed enormous resources, and resulted in few convictions. By the end, Congress allowed the independent counsel law to quietly die. Resurrecting this Frankenstein would once again strike a blow at the separation of powers, which protects individual liberty as surely as the Bill of Rights itself. It would also let Congress off the hook for conducting a vigorous probe and possible impeachment — the constitutional text’s only device to punish a sitting president.

Mr. Trump can short-circuit the Senate and shift the political momentum in his favor. Rather than fire Mr. Mueller, the president should promise his honest and complete cooperation with his nemesis, including agreeing to a one-on-one interview.

But Mr. Trump should also make clear that the special counsel must keep to his mandate — Russian meddling in the 2016 elections — and forget the unrelated payments to various mistresses, which, however sordid, do not relate to that investigation. If Mr. Mueller does not bring the investigation to a swift conclusion, Mr. Trump could then consider using his favorite line: “You’re fired.”