Updated at 4:46 p.m. ET

President Trump's firing of FBI Director James Comey has reignited calls for some form of independent investigation into Russian meddling in last year's election and possible ties to the Trump campaign. Comey confirmed in March that the FBI was looking into the matter (as are congressional committees).

But these calls come in various flavors.

Senate Democratic leader Chuck Schumer wants a "special prosecutor." He warns via Twitter, "If we don't get a special prosecutor, every American will rightfully suspect that the decision to fire #Comey was part of a cover-up."

Democratic Sen. Dianne Feinstein of California is calling for an "independent prosecutor." Feinstein says in a statement that she also supports the appointment of a "special counsel" by Deputy Attorney General Rod Rosenstein.

Republican Sen. John McCain of Arizona wants to see a "special congressional committee." That's not a new request from McCain, but he argues Comey's firing "only confirms the need and urgency of such a committee."

Republican Rep. Justin Amash of Michigan says he's leaning toward an "independent commission" to investigate Russian meddling.

Meanwhile, Senate Republican Leader Mitch McConnell is pooh-poohing all of these suggestions. On the Senate floor Wednesday morning, McConnell warned that a new investigation "could only serve to impede the current work being done" by the FBI and the Senate Intelligence Committee.

A little history

The first "special prosecutor" was Archibald Cox, who was appointed by President Richard Nixon's attorney general in 1973 to investigate the Watergate scandal. Cox was later fired in October of that year, along with Attorney General Elliot Richardson and his deputy, William Ruckelshaus. This was the notorious "Saturday Night Massacre" to which Comey's dismissal was immediately compared.

In the post-Watergate period, Congress passed the Ethics in Government Act, which formalized the procedures for appointing special prosecutors and also rebranded them as "independent counsels." Independent counsels were appointed by a three-judge panel at the request of the attorney general. Congress could also petition the attorney general to seek such an appointment, although the attorney general was not required to do so. The most famous independent counsel was Kenneth Starr, whose investigation ultimately led to the impeachment of President Bill Clinton. The Ethics in Government Act expired in 1999 and was not renewed.

Since 1999, the attorney general has occasionally appointed "special counsels" to investigate suspected criminal activity when an investigation by the Justice Department itself might pose a conflict of interest. Because these counsels are appointed by — and answer to — the attorney general, they have less formal independence than independent counsels.

One famous special counsel was Patrick Fitzgerald, who investigated and prosecuted Vice President Dick Cheney's chief of staff, Lewis "Scooter" Libby, for his role in the public identification of Valerie Plame, a covert CIA officer. (Libby was convicted on perjury and obstruction of justice charges. His prison sentence was later commuted by President George W. Bush.) The attorney general at the time, John Ashcroft, had recused himself from the matter so Fitzgerald was appointed by Ashcroft's deputy ... James Comey.