Washington (CNN) The tornado that was Rudy Giuliani's media appearances this week -- plus personnel changes to President's Donald Trump's legal team -- may signal a drastic change in how Trump will approach his legal strategy as the Russia investigation and a probe into Trump's personal attorney Michael Cohen swirl around the President.

Trump's legal team now consists of several accomplished attorneys with extremely disparate personalities. While Giuliani, who besides his political career is a former federal top prosecutor in Manhattan, captivated journalists with disclosures about Trump this week, three fresh lawyers who've shunned media attention are positioned to handle serious legal work to protect the President.

Many predict that Giuliani, as the face of the team, will seize opportunities to make news on TV and that he will be more aggressive toward special counsel Robert Mueller.

"Playing nice hasn't gotten them anywhere," a source familiar with the team said, going on to describe Giuliani as a "professional assassin."

Yet Giuliani's comments to Fox News about Trump's legal situations this week appeared to complicate the President's story. CNN reported Thursday that members of Trump's legal team -- which also includes a cluster of unofficial advisers, largely from Trump's New York social circle -- were caught by surprise when Giuliani spoke about Stormy Daniels, disclosing that Trump had reimbursed Michael Cohen for the adult film star's hush agreement.

The lack of clarity continued Friday, when Trump said Giuliani should "get his facts straight," and then the former New York mayor released a statement about what he said on Fox News, but didn't say who ultimately paid Daniels $130,000.

Other sources with knowledge of Giuliani's approach said his comments may have been planned to get ahead of the development if it were to leak. Aside from the drama of the Cohen investigation, which appears to be playing out in New York, Mueller's team and Trump's lawyers in Washington have been in talks about an interview between the special counsel and the President.

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Giuliani appeared to be in negotiation mode and interested in stoking a media frenzy Wednesday and Thursday, telling news outlets that any investigative interview of Trump wouldn't be longer than two to three hours and would have a narrow set of questions.

"Forget Bob Mueller, no respectable lawyer comes in and dictates what you're going to do. You don't go in and make demands," said Jon Sale, a Miami-based white collar lawyer and friend of Giuliani's. "You put forth reasonable positions to be persuasive."

Wednesday morning, the legal team had appeared to turn back toward more discreet lawyering, with the announcement that Washington trial lawyer Emmet Flood would join the team inside the White House.

Trump's Batman

Flood and other newcomers on Trump's legal roster could provide a counterpoint to Giuliani's New York bluster.

In all, Trump's team that responds to the Russia probe comprises Flood -- representing the office of the presidency from inside the White House -- and now the four private attorneys, Giuliani, Jay Sekulow, and Jane and Martin Raskin. The White House has its own counsel staff who handle day-to-day executive branch issues, and then the President has several other private lawyers assisting him, including in the criminal probe of Michael Cohen in New York and for civil lawsuits.

Flood may be the more experienced lawyer in the peculiar task of aiding a president under the pressure of a special counsel. The trial lawyer and former impeachment adviser to then-President Bill Clinton is taking an air-traffic-control-type position in the White House that has been held since last summer by Ty Cobb, who's retiring at the end of this month.

White House counsel Donald McGahn and his attorney Bill Burck, who is friends with Flood, lobbied Flood last weekend to join the President's team, according to a person familiar with the interaction. To make his case, Burck paraphrased the movie "The Dark Knight," telling Flood that he's Batman, the hero that Gotham -- the country -- deserves, this person said.

Flood leaves his law firm Williams & Connolly, among Washington's most elite trial powerhouses and which still represent the Clintons, to take the job. As of Friday -- two days into Giuliani's coup -- it wasn't clear whether Flood had started working at the White House yet.

A Chicagoan who early in his career taught high school English, Flood is a "tightly wrapped " individual who "couldn't get any further away from Trump's personality," according to a source familiar with the situation. Flood and his former law firm have been notoriously silent in response to media inquiries for years, and he did not respond to requests for comment this week.

Flood also served in a role similar to the position he's in now during George W. Bush's administration. In that role, he directed the White House's response to investigations.

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"My experience with him was he was clear-eyed, no nonsense, no sugarcoating, no bullshitting. Just giving you the straight reality of what you needed to do," said Scott Jennings, a former assistant to then-President George W. Bush whom Flood counseled during the congressional investigation into the firing of US attorneys.

While Jennings had a private defense lawyer help him prepare for Senate testimony -- Mark Paoletta, who's served as counsel to Vice President Mike Pence and general counsel of the Office of Management and Budget in the Trump years -- Flood sat with Jennings during his Senate testimony. Flood's job was to help Jennings and Paoletta decide when not to answer and assert executive privilege, the ability of a president to keep certain conversations and documents private.

"Having somebody like Emmet sitting behind you makes you feel a lot better about life," said Jennings, who's now a public relations executive and CNN contributor. "I think I'm the last sitting White House staffer to go to Capitol Hill and correctly invoke executive privilege on behalf of the president."

Assertions of privilege -- the ability to decline to answer and keep information secret -- could include the president claiming executive branch confidentiality, protecting attorney-client discussions and pleading the Fifth Amendment right against self-incrimination. All could become an avenue for future negotiations and court fights -- especially if Mueller interviews Trump or subpoenas him to testify before a grand jury.

Not showboats

Among Trump's personal attorneys, Jay Sekulow, a conservative radio host and nonprofit legal organization head, soldiers on after surviving the turmoil of Marc Kasowitz stepping back, John Dowd exiting and the husband-and-wife duo of Victoria Toensing and Joe DiGenova never securing the job. Sekulow added Giuliani and now may step back, according to sources familiar with the team.

The Raskins, brought aboard after several top Washington lawyers turned down working for Trump, couldn't be more different from Giuliani. "They're not grandstanders," Sale said. Another Florida white collar lawyer who knows both the Raskins and Giuliani described the couple similarly, as "not showboats."

"You're not going to hear speeches about the government being crazy from them," the lawyer said.

Still, Giuliani will likely work closely with the Raskins, who are well-respected especially among Florida lawyers for their criminal defense work.

"Behind the scenes, anybody as smart as Rudy knows you need to brainstorm with other people on your team and make it a collaborative effort," Sale said.

The Raskins have specialized in criminal defense, primarily in Florida federal court, for years. They've cut plea deals for clients, defended people caught in conspiracy and fraud investigations, and run their own firm out of Coral Gables, almost two hours south of Mar-a-Lago, where they met with Trump last month, according to The Washington Post. Jane Raskin worked decades ago with Mueller and with James Quarles, a prosecutor negotiating the interview with Trump.

"One thing about the Raskins is they're very easy to work with," said the lawyer who's friendly with them, declining to give his name or law firm.