(CNN) White House chief of staff John Kelly has been omnipresent during President Donald Trump's first appearance at the United Nations General Assembly this week, a multiple-day foray into the complicated world of international politics.

The message has already been heard back in Washington.

A half-dozen Republicans inside and outside the White House tell CNN that Kelly's efforts to rein in an unruly West Wing have started to show results.

The President is still surrounded by people who feed his impulsive tendencies, such as Dan Scavino, his social media director who regularly helps Trump fire off some of his most controversial social media missives.

But as much as Trump is not retreating from the rhetoric and tone that helped win him the White House, sources say the President has also begun to make a conscious shift in his approach to governing after months of failing to score a sweeping legislative victory.

Out -- for now -- are the days of Trump sending nasty tweets at Republican lawmakers , such as Sens. John McCain of Arizona and Lisa Murkowski of Alaska.

In -- CNN reported Monday -- is outreach to lawmakers whose relationships with the White House have frayed, including Murkowski, as well as Democratic leaders.

Personalities

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To help with this effort Kelly has enlisted staff secretary Rob Porter, a longtime Capitol Hill aide whose stock is on the rise inside the White House. Republican sources say Porter helps Kelly vet what information gets to the President's desk and what gets stopped at the door.

Concerned by the top-heavy, sprawling organization when he took over, Kelly began interviewing aides to determine what they did, how much access they had to the President and whether that access was deserved.

Kelly is now putting what he learned into practice, sources tell CNN, restricting access to the President, watching the information put in front of Trump and limiting the power of top aides.

"In the old days, you would arrive and the door to the Oval office would be open ... and the door behind you would stay open, and people were still wandering in and out -- staff, kids, grand kids," one GOP senator who has made multiple visits to the White House both before and after Kelly told CNN.

Now during visits, the senator said, the visits are much more formal.

"When we walked in the Oval Office door was closed. The President was sitting alone at his desk," the senator said. "We had our meeting, no one came in or out. It was all business."

Some aides, such as former adviser Sebastian Gorka and former White House strategist Steve Bannon, were let go altogether.

Longtime confidante Keith Schiller left his White House position Tuesday, according to multiple sources. He had told associates he planned to leave the White House because of income concerns, other sources told CNN. But he shared plans to leave just over a month after Kelly became chief of staff with the mission of instilling new order.

Trump, to be sure, is still very much himself with Kelly as chief of staff. The President recently stood by his comments equivocating blame between white supremacists and protesters in Charlottesville, Virginia, retweeted an offensive gif of Hillary Clinton and delivered a bellicose, nationalist speech to the world on Tuesday at the United Nations.

But Republicans across Washington say they are noticing changes within the White House's operations.

Even so, Kelly has told associates he has no interest in trying to control the President -- any such effort, he adds, would surely fail.

In fact, Trump still talks to outside advisers -- like Bannon -- and longtime friends on the phone, giving those who hope to influence Trump a back door into the White House.

Republican sources outside the West Wing who are pleased that Kelly is asserting his control acknowledged that the chief of staff can only do so much. Trump's cell phone use, which usually happens in the confines of the President's private residence, shows no signs of abating.

Policy

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Kelly works from a stand-up desk in his corner office of the West Wing, just down the hall from the Oval Office. A single portrait of President Abraham Lincoln hangs on the wall, with a bronzed sculpture of the flag-raising at Iwo Jima providing the only decoration in the second-best piece of office real estate in the building.

Even though there is no playbook for a Trump presidency, Kelly has sought the advice of former White House chiefs of staff Rahm Emanuel and Leon Panetta, Democrats, and Andy Card and James Baker, Republicans.

"He doesn't care how long he stays. That's what makes him effective -- for now," a Republican close to the White House said, noting that the biggest open question in Washington is whether -- or how soon -- Trump will chafe under Kelly's stern hand.

So far, Trump has responded by ever-so-slightly moderating on policy, taking less hardline positions than he previously held and signaling a willingness to work with Democrats on immigration or tax reform.

Kelly's fingerprints are firmly on this new outreach to Democratic congressional leaders, with Kelly convincing Trump that he could be seen as trying to rise above the partisan gridlock of Washington. It was a sales pitch Trump accepted, aides say, in part because of his anger at the Republican-controlled Congress.

"This wouldn't have happened without Kelly," a White House official said, speaking on condition of anonymity to avoid violating Kelly's biggest pet peeve: talking to reporters.

Some of the changes have earned Trump the scorn of his base. Breitbart, the conservative publication run by former Trump aide Steve Bannon, labeled the President "Amnesty Don."

But to those now surrounding Trump in the White House, the criticism is worth the chance of scoring a major legislative win.

Protection

Kelly has also made his presence felt by deciding which White House staff gets Secret Service protection, according to two sources with knowledge of the move.

White House counselor Kellyanne Conway, a Trump aide who received Secret Service protection starting in January, no longer has the constant security, sources tell CNN.

The move is part of a broader review -- initiated, in part, by Kelly -- of who really needs protection in the White House, sources said. Part of the review is aimed at helping an operation that has been stretched thin by the demands of Trump's sprawling family.

But Kelly, according to a source, also wanted to review which positions inside the White House warrant protection.