When Donald T. Regan resigned as chairman of the world's biggest investment firm, Merrill Lynch, to become secretary of the Treasury, he turned to a little-known investment firm to manage his considerable wealth.

Regan's assets--more than $3 million at the time he took the job, according to estimates based on government disclosure statements--were placed in a blind trust managed by the Bessemer Trust Co.

There is no public report on Regan's blind trust, but judging the figures Bessemer does publish, Regan probably has made out handsomely.

Bessemer's major equity fund, for example, has enjoyed a 25 percent average annual return during the past three years. Pensions and Investment Age, a trade publication, rates the performance of Bessemer Trust's equity funds in the top three of such funds over the past 10 years.

That kind of appreciation should be enough to have would-be clients lining up in front of Bessemer's appropriately staid Fifth Avenue offices. It turns out there is no line, however. Bessemer deals only with those who have at least $1.5 million to invest.

Actually, Bessemer can afford to be choosy, thanks to the $1 billion birthright it manages belonging to the 154 direct descendants of steel magnate Henry Phipps, the one-time partner of Andrew Carnegie. Phipps sold his interest in Carnegie Steel in 1905 for $50 million to J. P. Morgan, who went on to form U.S. Steel. Phipps then used $5 million of that money to form Bessemer Trust, named after Sir Henry Bessemer, inventor of the steel conversion process.

Unlike many other multimillionaire American families, such as the Fords, the Kennedys and the Rockefellers, the Phipps have avoided public attention. Perhaps the best known Phipps is Ogden Mills "Denny" Phipps, chairman of Bessemer, who is well known in sporting circles for his horse breeding talents and as chairman of the New York Racing Authority.

For decades, Bessemer Trust serviced only family members from three separate Bessemer trust firms located where the Phipps family clustered--Florida, New Jersey and New York. Bessemer executives were responsible for the family's care and feeding, doing everything from paying gardeners and buying theater tickets to closing winter homes and balancing check books.

The youngest of Henry Phipps' five children died last spring, a month short of his 100th birthday. But the function of the trust began to change back in 1974, a change forced by economic realities and approved by the Phipps' heirs.

Said John R. Whitmore, president of the trust: "Until the mid-1960s the trust operated with a few key people. But after that, we began needing specialists to deal with complex problems."

Whitmore said that, for instance, the trust had to maintain a full-time staff to settle estates at a cost of about $400,000 a year--although there was a six-year period when no Phipps family members died.

Whitmore, 48, who has the kind of solidly conservative demeanor one expects of a man in that job, was hired to run the revamped Bessemer Trust in 1975 from American Security Bank in Washington, where he was deputy chief of the trust department.

Now Bessemer has $2.5 billion in assets under management, from 500 individual clients, including the Phipps descendants, and 100 institutions. "It's a unique owner-client relationship," said Robert C. Elliott, executive vice president who also is an alumnus of American Security. "The Phipps family are willing to pay well, and all the clients get the same quality of service."

Beginning two years ago, the Phipps family initiated a plan to share with about a dozen managers of the fund up to 45 percent of the profits from fees charged to clients. The minimum fee is $15,000 a year to manage $1.5 million.

Investing money for U.S. and foreign clients' employe-benefit plans is a major part of the business. There also is Bessemer Securities Corp., a venture capital firm that invests only Phipps family money.

The Bessemer interests also are involved in offshore finance through Overseas Private Equities N.V., which is based in the tax haven of the Netherlands Antilles. OPE attracts venture capital from institutions in Switzerland, Spain, Germany, Britain and Luxembourg, according to Whitmore.

The search for promising ventures--often investments in young or troubled companies--is carried out by Bradford Associates. Bradford, a related firm that works exclusively for Bessemer interests, follows up on the investments, often putting people on the boards of directors of companies in which Bessemer invests.

"Typically, we will invest in debentures convertible into stock after a period of years. The company gets money below the going interest rate and we have the option of taking a controlling interest in the company," said Whitmore.

Said Elliott, "We want to harvest our investment as quickly as we can."

They point to Moxie, the old soft drink company, as an example of what can come from a Bessemer investment. "We helped the company find a German investor, who bought our shares and made an additional investment in the company. Now Moxie is involved in producing vitamins and a lot of other things," said Whitmore.

How is Besemer investing these days? "We're defensive today," said Elliott. "This is not an environment in which aggressive investors will be rewarded. We like interest-sensitive issues, regional and money-center banks, utilities, which should benefit from declining interest rates and regulatory requirements. But we're hedging our bets, going for assets that can be quickly liquidated."

Does Bessemer still offer the personalized, hand-holding service it used to provide for the Phipps family?

"We now say we will provide any reasonable services for clients," said Elliott, stressing the word reasonable. "If they have a car wreck, for example, we will help them solve their problems."