As problems go, this is a pretty good one to have.

Gary Barnett, the developer of One57, is attracting a steady flow of billionaire buyers to his Midtown tower, which upon completion next year will be New York’s tallest building with residences.

But Mr. Barnett, the president of the Extell Development Company, is more than a little worried about a possible gripe fest in the tower’s top 15 floors, where the billionaires’ club is forming.

Several of the future owners of the high-altitude, full-floor apartments are hiring their own designers to finish their spaces, which could become a big headache for their neighbors, Mr. Barnett said.

“This was a major, major issue for us,” he said. “We don’t want our people who are buying and accepting our finishes to be sitting there for three or four years while tons of construction goes on in the building and people build out their spaces. It ties up elevators and creates dust and noise. We are doing everything possible to avoid that.”

Buyers of the two duplex penthouses, and a number of the other purchasers of the seven full-floors that have been sold so far (out of a total of 11), are planning to finish their spaces themselves, Mr. Barnett said.

They include the fashion moguls Silas K. F. Chou and Lawrence S. Stroll, the first billionaires to be identified as buyers a week ago, according to a person familiar with the matter.

Mr. Stroll, a 53-year-old Canadian, became a billionaire after he and Mr. Chou, 66, took the fashion label Michael Kors public last December as the company’s majority owners and former co-chairmen, cashing out hundreds of millions of dollars of their shares. Mr. Stroll is worth an estimated $1.8 billion, while Mr. Chou, the son of a billionaire from Hong Kong, has a fortune of $2 billion, according to Forbes.

The longtime friends and business partners, who also previously acquired and served as co-chairmen of the Tommy Hilfiger Corporation, were among the first buyers at One57. According to two people who declined to be identified because of confidentiality agreements, Mr. Stroll bought first; his 85th-floor unit, with four bedrooms and 6,240 square feet, cost just under $50 million. Mr. Chou bought the 82nd floor for just over $50 million, they said.

One other buyer at One57 was identified last week. He is Michael Holtz, the owner of the SmartFlyer travel agency; he said he had bought a three-bedroom apartment on the 39th floor facing Central Park, but would not disclose the price.

Mr. Holtz, who is on the advisory board of the Park Hyatt, the hotel that will be under the One57 condo residences, said in an interview that he is not a billionaire. (Michael Gross, who is writing a book on 15 Central Park West and has a blog, was the one who identified Mr. Holtz as a buyer.)

He brings to four the number of identified individuals who have bought in so far.

Richard Kringstein, co-owner of the Herman Kay Company, which makes women’s and men’s clothing, was the first to become known; he bought a three-bedroom residence for an undisclosed price.

“It will make for good dinner conversation once we all move in, right?” Mr. Holtz told me this week.

Mr. Barnett said that most buyers below the top 15 floors so far want the Extell finishes by the Danish designer Thomas Juul-Hansen, rather than to finish the spaces themselves.

Some are not sure they will even move in. Mr. Holtz never lived in an apartment he bought at 15 Central Park West. Less than two months after closing on it for $4.86 million in early 2008, he flipped it for a $3.6 million profit.

“This is going to be a hard one not to live in,” Mr. Holtz said of One57. “Maybe I will stay, maybe I won’t, maybe I’ll rent it. It really depends on what mood I’m in.”

But up in the billionaires’ club, there is sure to be some commotion. To head off any grumbling, Mr. Barnett said he struck agreements with the full-floor purchasers that would allow Extell to do a lot of the “heavy work” — like stones, plasterboard and studs — while finishing the building. Extell is trying to accelerate construction so that the lower-floor residents can move in by the summer of 2013 and the owners on the upper floors can start moving in by the end of that year.

The developer has taken a hard line with some potential buyers. Mr. Barnett said he passed up one full-floor sale after protracted discussions with the prospective buyer about his plans to finish the space. “The guy wanted to do his own stuff and wouldn’t let us do what we were going to do,” Mr. Barnett said. “I said, ‘Forget it, I don’t want to go through with this.’ ”

Mr. Barnett ultimately set a signing deadline for the buyer, a Russian billionaire, according to one person familiar with the matter. The Russian missed the deadline, but he later agreed to include Extell in his construction plans. By then Mr. Barnett had moved on.

Such design skirmishes are not uncommon for the superwealthy in New York. Developers sometimes deliver apartments “raw,” or with the minimum fixtures and plumbing legally allowed, so that buyers can do their own custom work. That was true, for example, of the penthouse at 15 Central Park West owned by Daniel S. Loeb, the hedge fund manager.

New York developers sometimes offer modest credits to high-end buyers who choose to finish their own apartments, but it is not a common practice, said Jonathan J. Miller, the president of Miller Samuel, a property appraiser. From the developers’ standpoint, any potential cost savings on labor and materials is often outweighed by the disruption that individual projects can cause, he said.

Many high-end co-ops on Fifth and Park Avenues have summer work rules, which allow extensive renovation only between Memorial and Labor Days (when they assume most residents are in the Hamptons). “If they don’t get it done,” Mr. Miller said, “they have to wait another year.”

Mr. Barnett had an earlier flap over custom construction with Nick Candy, a developer of One Hyde Park, the superluxury apartment development in London. Mr. Candy, while giving me a tour of his penthouse there in June, expressed concern about there being just three elevators for the condo residences at One57 (the Park Hyatt will have separate elevators). “We were worried that it would be a building site for 10 years afterwards,” Mr. Candy said. “You haven’t got enough lifts to get the renovations done.”

Mr. Barnett said the elevators were “absolutely fine.” He refuted — by showing me e-mails — Mr. Candy’s claim that he had pulled out of a deal to buy two apartments at One57 over the issue of elevators. In fact, the deal died after Mr. Barnett refused to give Mr. Candy rights to flip his contracts before construction was completed. “He was trying to pull a fast one,” Mr. Barnett said.

Still, was Mr. Candy’s supposed concern about elevators altogether misplaced?

After all, the three elevators will have to service all of the tower’s 92 apartments. Normally, three would probably be enough in a building that size, Mr. Miller said.

They will be fast, taking only 30 seconds from the ground floor to the top of the 1,004-foot building, according to Extell. And most, if not all, of the full-floor buyers have homes in other places, meaning they can wait out any construction chaos if they choose.

Even so, there is probably still confusion to come. Mr. Barnett is keen to head off a problem in the billionaires’ club over all the work crews and noise — especially since he knows that custom finishing work for billionaires can go on for two or more years.

But he already has more than $1 billion in sales in contract at One57, and he says he has sold about 60 percent of the residences.

Good news, as he knows, almost always comes with an asterisk.