President Donald Trump's stunning firing of FBI Director James Comey Tuesday triggered renewed demands from lawmakers, former government officials and watchdog groups for an "independent" investigation into possible ties between Trump campaign associates and Russian meddling in the 2016 presidential election.

For months, some have argued for the appointment of a " special" counsel or prosecutor , while others want to form a congressional " select committee ," and a third group suggests launching a new bipartisan commission . While none of these options are mutually exclusive, there are, however, significant differences in the purpose, scope and viability of these approaches.

Here's a breakdown of the various paths available and how they differ:

Special counsel

Attorney General Jeff Sessions decided in March to recuse himself from any existing or future investigations related to Trump's presidential campaign ( or transition ) after reports surfaced that Sessions had met with a Russian diplomat last year. As a result of Sessions' recusal, Deputy Attorney General Rod Rosenstein is now overseeing the FBI's investigation into whether there was any coordination between the Trump campaign and Russian interference in election.

The attorney general's regulations provide for appointment of outside " special counsel " in certain circumstances, including if handling by the Justice Department would "present a conflict of interest for the department or other extraordinary circumstances," and if "it would be in the public interest to appoint an outside special counsel to assume responsibility for the matter."

In light of Sessions' recusal, however, the decision to appoint a special counsel in this case will rest solely with Rosenstein.

And while lawmakers on Capitol Hill have no role in the appointment of any special counsel, that hasn't stopped top Democratic leadership from putting pressure on Rosenstein to appoint someone else in his place.

"Deputy Attorney General Rosenstein sat in the Judiciary Committee and promised to appoint a special prosecutor at the appropriate time," Senate Minority Leader Chuck Schumer said Tuesday. "That time is right now. The American people's trust in our criminal justice system is in Rosenstein's hands. Mr. Rosenstein, America depends on you to restore faith in our criminal justice system, which is going to be badly shattered after the administration's actions today."

Experts say the main purpose of a special counsel in the Russia situation would be the pursuit of an independently driven criminal investigation.

"They can utilize a grand jury, they can ask to return indictments, they would be empowered to pick staff (of their choosing), and provided with a budget to carry out responsibilities," said attorney Richard Ben-Veniste, who served as the former chief of the Watergate Special Prosecutor's Watergate Task Force and on the bipartisan 9/11 Commission.

In other words, the goal of an investigation conducted by a special counsel "is not to answer public questions about what happened or what may still be happening," as Wittes wrote in a post on Lawfare , but rather to conduct "a set of foreign intelligence and counterintelligence investigations that may (or may not) have criminal investigative elements."

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Select committee

While a number of House and Senate committees are currently examining Russian interference in the election, Arizona Sen. John McCain and other outside experts have specifically called for a "select committee," with new members hand-picked by current congressional leadership.

In the immediate aftermath of Comey's firing, such calls grew louder.

"I have long called for a special congressional committee to investigate Russia's interference in the 2016 election," McCain said in a statement Tuesday. "The President's decision to remove the FBI Director only confirms the need and the urgency of such a committee."

Advantages of using such a select committee include newly dedicated staff with sufficient expertise and time, subpoena power to compel testimony and documents, and ideally, implementation without the arguable taint of influence by the White House -- an accusation that has besieged existing structures like the House intelligence committee's investigation.

While both a special counsel and a select committee could employ certain investigative functions, Wittes cautions that they serve different purposes: The special prosecutor function is "designed to prosecute crimes," whereas a select committee is "designed to do an investigation so that Congress would know how to pursue it's constitutional functions."

But Caroline Fredrickson, president of the American Constitution Society, said the choice between a special counsel and a select committee "shouldn't be either/or," despite the fact that "there are somewhat different interests being protected" -- both approaches are useful "given that the stakes are so high here."

Bipartisan commission

On the other end of the spectrum, some have called for a new bipartisan independent commission to investigate Russia's influence on the election, much in the same vein as the 9/11 Commission.

Rep. Eric Swalwell, a California Democrat who sits on the House intelligence committee, accused the White House in March of "obstructing" the panel's investigation, and called repeatedly for an independent commission to review the matter.

The purpose of such a commission is distinct from a criminal investigation, as its goal would be "inform the legislature or the public about something that happened," Wittes said. "The purpose of the 9/11 Commission was to tell the story of how we got to this point."

"The advantage is that it's flashy and very independent," but it's "not well-positioned to litigate" without certain investigative powers, Wittes added.

The other downside of an independent commission is that it would require legislation to enact, which could prove challenging in the current political climate.

If used, "it would no doubt be the result of substantial public pressure on Congress and the President, but it seems unlikely at this point," Ben-Veniste said.