Still, the family’s tax planning was effective enough that after Estée Lauder died in 2004, she passed down nearly $4 billion to her heirs, according to tax experts who studied the case and estimated that the estate was taxed at an effective rate of 16 percent — about a third of the top estate tax rate at the time.

Ronald Lauder has not been a director of the company since 2009, but he still serves as the president of its Clinique Laboratories subdivision. He also sublets a full floor of office space from Estée Lauder, on the 42nd story of the General Motors Building in Manhattan, which serves as the hub for the matrix of foundations, investment funds, partnerships and trusts used to control his businesses and personal finances.

His stake in Estée Lauder Companies, according to regulatory filings, is valued at more than $600 million. Nearly $400 million of that stock is pledged to secure various lines of credit. Many financial planners consider it imprudent for principal shareholders in a company to borrow against their stock. But it remains a popular way for wealthy taxpayers to get cash out of their holdings without selling and paying taxes.

There is a certain irony that Mr. Lauder has used $72 million worth of his Estée Lauder shares to carry out his latest state-of-the-art tax reduction tactic. These contracts emerged as a popular tool about a decade ago and were developed by accountants and tax planners after Congress closed down the loophole on the Estée Lauder public offering. The I.R.S. began cracking down on these contracts in 2008, and has pursued a prominent case against the billionaire Philip Anschutz, who used one to avoid more than $140 million in federal taxes.

Whether or not the I.R.S. agrees with Mr. Lauder’s contention that his contract is legitimate, some tax policy experts say the deal illustrates how the wealthy take advantage of the system.

“There’s real truth to the idea that the tax code for the 1 percent is different from the tax code for the 99 percent,” said Victor Fleischer, a law professor at the University of Colorado. “Any taxpayer lucky enough to have appreciated property is usually put to a choice: cash out and pay some tax, or hold the property and risk the vagaries of the market. Only the truly rich can use derivatives to get the best of both worlds — lots of cash and very little risk.”

While Mr. Lauder’s stock holdings in publicly traded companies show some of his tactics, much of his wealth is harder to examine because it is controlled by a maze of privately held trusts and companies. Court documents, S.E.C. filings and property tax records spotlight a few of the more ordinary tax breaks used by affluent people.