There are currently three main investigations into Russian interference in the 2016 presidential election and possible ties to the campaign of President Trump. They all have some issues.

Fact-finding investigations Criminal investigation House Intelligence Committee Senate Intelligence Committee F.B.I. Asks what happened. Produces report. Asks if laws were broken. Could result in criminal charges. Fact-finding investigations Criminal investigation House Intelligence Committee F.B.I. Senate Intelligence Committee Asks what happened. Produces report. Asks if laws were broken. Could result in criminal charges.

The independence of the Senate and House investigations has been called into question, in large part because the president’s party controls both chambers of Congress.

Led by Republican Chairmen House Intelligence Committee Senate Intelligence Committee 13 Republicans

9 Democrats 8 Republicans

7 Democrats Devin Nunes Recused himself after improperly sharing information with White House. Richard Burr Mike Conaway Leading House investigation after Mr. Nunes’s recusal. Led by Republican Chairmen House Intelligence Committee Senate Intelligence Committee 13 Republicans

9 Democrats 8 Republicans

7 Democrats Devin Nunes Recused himself after improperly sharing information with White House. Richard Burr Mike Conaway Leading House investigation after Mr. Nunes’s recusal.

At the same time, the leadership of the Justice Department, which is in charge of the F.B.I. investigation, has also been marred by politics.

Attorney General Jeff Sessions Key role in Mr. Trump’s campaign. Recused himself from Russia investigation. Acting Attorney General Sally Q. Yates Fired by Mr. Trump for refusing to defend in court his original travel ban. She previously warned the White House that Michael T. Flynn was vulnerable to blackmail because he misled his bosses about conversations with a Russian official. Deputy A.G. Rod J. Rosenstein Wrote White House memo used to justify firing James B. Comey. F.B.I. director James B. Comey Fired by Mr. Trump. Attorney General Jeff Sessions Key role in Mr. Trump’s campaign. Recused himself from Russia investigation. Acting Attorney General Sally Q. Yates Fired by Mr. Trump for refusing to defend in court his original travel ban. She previously warned the White House that Michael T. Flynn was vulnerable to blackmail because he misled his bosses about conversations with a Russian official. Deputy A.G. Rod J. Rosenstein Wrote White House memo used to justify firing James B. Comey. F.B.I. director James B. Comey Fired by Mr. Trump.

The firing of Mr. Comey added a new circular conflict to deal with.

President Trump who said the Russia investigation was on his mind when he fired Mr. Comey who will oversee the investigation into possible collusion between Russia and the campaign of will appoint a new F.B.I. director President Trump who said the Russia investigation was on his mind when he fired Mr. Comey who will oversee the investigation into possible collusion between Russia and the campaign of will appoint a new F.B.I. director

Democrats and others have been calling for an investigation that would be considered less partisan. On Wednesday, Deputy Attorney General Rod J. Rosenstein appointed Robert S. Mueller III to serve as a special counsel. Here’s how the special counsel compares to other possible investigatory bodies:

Fact-finding investigations Criminal investigation Select Committee Independent Commission Special Counsel Bipartisan, made up of members of Congress. Bipartisan experts from outside government. Appointed by Justice Department. Example: House Benghazi committee 9/11 Commission Robert S. Mueller, former F.B.I. director. Fact-finding investigations Criminal investigation Independent Commission Select Committee Special Counsel Bipartisan, made up of members of Congress. Appointed by Justice Department. Bipartisan experts from outside government. Example: House Benghazi committee Robert S. Mueller, former F.B.I. director. 9/11 Commission

The select committee and special counsel are easier to initiate than an independent commission because they do not require Mr. Trump’s signature. However, some legal experts consider them potentially less independent than other options.

Fact-finding investigations Criminal investigation Either the House or the Senate can create a … The Justice Dept. appoints a … Both the House and Senate pass a bill. President signs the bill, creating an … Select Committee Special Counsel Independent Commission Work culminates in report. Work culminates in report. Could result in criminal charges. Fact-finding investigations Criminal investigation Either the House or the Senate can create a … Both the House and Senate pass a bill. The Justice Dept. appoints a … President signs the bill, creating an … Select Committee Special Counsel Independent Commission Work culminates in report. Work culminates in report. Could result in criminal charges.

A select committee would be made up of current members of Congress and therefore has the potential to be more political than an independent commission, which would be filled with outside experts. Both of these options would have fact-finding missions.

While Mr. Mueller will enjoy more day-to-day autonomy than a United States attorney usually has, he still falls under the supervision of the attorney general — or in this case, Mr. Rosenstein — who could overrule important decisions.

There is also precedent for the department to waive those regulations and appoint a special counsel with greater independence.

In 2003, Mr. Comey was the deputy attorney general and was overseeing an investigation into the leaking of a C.I.A. operative's identity because Attorney General John Ashcroft was recused.

Mr. Comey chose to waive the regulations and appointed Patrick Fitzgerald, then the United States attorney in Chicago, as special counsel, and delegated to Mr. Fitzgerald his supervisory powers as the acting attorney general for that case.

However, the president could order the firing of either type of special counsel.

Some experts say the best option could be one that no longer exists. The law under which independent counsels were appointed was enacted in the years after the Watergate scandal in an attempt to ensure the independence of inquiries into possible misconduct by top executive branch officials.

It gave the judiciary branch, rather than the executive, direct control — meaning the person could not be fired by the president.