Washington (CNN) President Donald Trump's senior aides have further restricted the number of administration officials allowed to listen to the President's phone calls with foreign leaders since his July 25 call with Ukraine's President was revealed and became the centerpiece of the impeachment inquiry , according to multiple White House sources.

Transcripts of Trump's calls with world leaders are also disseminated to a far smaller group of people inside the White House, those administration sources say, continuing an effort to limit the number of people with insight and information about the conversations.

It amounts to a concerted effort to prevent Trump's conversations -- which officials have said sometimes veer off into unguarded or undiplomatic territory -- from becoming known to even those inside the administration.

"Nobody is allowed on the calls," a White House official said, describing the new effort to limit those with access to the calls to only the President's senior-most aides, barring some senior and mid-level career staff from listening in. "The barn door officially closed after the horse escaped."

Earlier in the administration, and during past presidencies, a larger number of officials would be allowed to listen to phone calls with foreign leaders. That includes aides with specific expertise in the countries being phoned or officials focused on an issue set being discussed on the call.

Now, when the President speaks on the phone with world leaders, he's joined on the call by just a handful of others appointed by Trump to the highest level of the administration, multiple White House officials say. The list is signed off on by national security adviser Robert O'Brien, who will often join the call himself along with a rotating roster of officials including his deputy Matt Pottinger, Secretary of State Mike Pompeo, acting chief of staff Mick Mulvaney and his deputy Rob Blair.

Vice President Mike Pence's national security adviser Lt. Gen. Keith Kellogg is often the sole representative from Pence's office.

Gone from the calls are some of the career staffers and detailees whose roles included taking notes and providing edits to the eventual transcript of the conversations meant to clarify what was said.

While limiting access to the President's phone calls is designed to stop leaks and tamp down on dissent internally, the official said, it results in "a smaller circle of loyalists in all policymaking discussions" which could have a serious impact on how the administration executes its foreign policy, according to experts.

Another White House official jokingly called the change "The Vindman Rule," after Lt. Col. Alexander Vindman, the National Security Council's director on Ukraine.

Vindman was among those who listened to the July 25 call from the Situation Room. He found the call so concerning that he reported it to National Security Council lawyers. The call was also the foundation for the whistleblower complaint that was filed by a member of the intelligence community and which formed the basis for the impeachment inquiry.

Last month, Vindman testified to the House Intelligence Committee that he felt the call was "improper" and that it undermined US national security.

"Vindman wouldn't hear the (July 25th) call if it happened tomorrow," the first White House official told CNN. Vindman is still detailed to the National Security Council from the Pentagon. Despite speaking out against Trump, he continues to work on Ukraine matters at the White House.

Trump appeared to be referencing Vindman on Friday when he insisted his phone call with Ukraine's President was "perfect."

"I'm lucky we had this transcript, which, by the way, has been verified by the lieutenant colonel -- the lieutenant colonel, OK?" Trump said, emphasizing the word "lieutenant" in Vindman's title. "He's another beauty."

Reducing access

Trump's aides have previously taken steps to reduce the number of people on his foreign leader calls. In 2017, leaked transcripts of calls Trump had with the leaders of Australia and Mexico embarrassed the White House and the national security adviser at the time, Gen. H.R. McMaster, made moves to restrict who could listen in.

Some of those restrictions were loosened when the role was taken over by Ambassador John Bolton, who favored traditional protocol and process.

Like O'Brien, Bolton also approved who could participate on the calls but allowed a wider list of officials. The July 25 call, which was "expected to be routine," according to the whistleblower, included not just Vindman but the vice president's adviser on Russia, Jennifer Williams, as well as a National Security Council press aide and White House Situation Room staff in charge of the summary of the call.

Now, those senior national security officials who are responsible for managing relations and policy with the specific region or country -- such as Vindman and Williams -- are excluded, as well as lower "working level" staff.

"It's rare that anyone who's not a political appointee sits in on a live call," a White House official said, drawing a distinction between the political staff appointed by Trump and careerists who serve in administrations of both parties.

A National Security Council spokesperson would not comment on the record.

National security experts said fewer people listening in to calls with world leaders could significantly impact the execution of agreed-upon policies.

"Some big decisions come out of meetings between the President and foreign leaders that bear on policy direction," says Eric Brewer, a former director for counterproliferation on Trump's National Security Council, who also worked under President Barack Obama. "NSC staff are the connective tissue between the White House and interagency. So giving a readout of these calls and meetings to the interagency is critical to getting things done."

Classified server

After Vindman complained to the top National Security Council lawyer, John Eisenberg, about the July 25 call, Eisenberg placed the transcript on a highly classified server, limiting access to only those with high-level specific clearance.

Now, transcripts of Trump's phone calls often go only to top principals in the administration, including to Pence and Trump himself.

Those who would traditionally need access to the transcripts can no longer find copies that have been housed in an easily accessible system, one official said. Another person familiar with the matter said the transcripts are still being vetted and reviewed by several layers of National Security Council officials.

The changes have been coupled with radical cuts to the National Security Council under O'Brien, who was instructed by Trump to slash the size of the council.

O'Brien told staff he plans to reduce the agency's size by about half -- to around 120 people -- by early 2020. O'Brien said the National Security Council had "ballooned" under Obama and told Fox Business he wanted to get it back to "about 100" which was the size under President George W. Bush. Many career officials detailed to the National Security Council from various departments and agencies will not be replaced when their assignments are up.

Trump hinted publicly at his desire to cut back on those who could participate in his calls amid hearings in the House impeachment inquiry, saying that some of the most damaging testimony against him came from people he doesn't know -- including Vindman, whose credibility stemmed from their apolitical roles and proximity to Trump's calls, White House officials previously told CNN.

"National security professionals seeking to advance US policy objectives may or may not reflect or even be aware of Trump's personal views, which are often divorced from a rational process and center on Trump's own obsessions and political interests at the expense of the national interest," Colin Kahl, a former national security adviser to Vice President Joe Biden, said. "Cutting subject matter experts and professionals out the loop will make this problem worse."