To most people, Procter & Gamble is known for powerhouse brands such as Tide, Tampax and Pampers. But to people whose stomachs churn when American companies go to great lengths to avoid taxes, there’s a more appropriate P&G product: Pepto-Bismol.

My stomach got a bit queasy when I examined P&G’s deal to sell 43 beauty brands to Coty, the big beauty company, for $12.5 billion (what Coty said it’s paying) or maybe $15 billion (the deal’s value the day it was announced last week).

Either way, the transaction is a thing of beauty to tax techies — although not to regular taxpayers. P&G is using a “Reverse Morris Trust” to avoid billions in taxes that it would have owed in a straight-up sale of the brands, which include Wella, Clairol, Max Factor and Covergirl.

P&G shareholders must have a majority of the stock and voting power in New Bigger Coty to get tax-free treatment. Coty can make that deal because the Reimann family of Germany, which owns two-thirds of its stock, will own about a third of the new company, leaving it firmly in control.

P&G plans for its shareholders to swap more than $10 billion in P&G shares to P&G in exchange for shares in New Bigger Coty. That would be a good chunk of the $70 billion P&G says it will give shareholders in dividends and stock buybacks over the next four years.

The Proctor & Gamble headquarters complex in Cincinnati. Coty is buying 43 beauty brands from Procter & Gamble Co., including Miss Clairol, Covergirl and Max Factor. (John Minchillo/AP)

P&G is saving about $2 billion to $4 billion in taxes (by my estimate) via this technique. In return for leaping through hoops, Coty is presumably paying less than a straight-up purchase would have cost, in effect sharing in P&G’s tax savings.

This will be the third Reverse Morris Trust — or RMT, as tax types call it — that P&G has pulled off. “They’re the unchallenged market leader when it comes to this technique,” says tax expert Robert Willens of Robert Willens LLC. “P&G has developed an affinity for RMTs the likes of which has never been seen before.”

Proving that someone involved in the deal has a sense of humor — or perhaps a sense of irony — P&G is calling the entity that will hold the to-be-disposed-of products RMT Brands. The name may change later, but it’s smile-making now.

P&G did its first RMT in 2002, selling Jif peanut butter to the Smucker jelly company, which I called the merger of PB with J. In 2008, P&G sold Folgers to Smucker in a second RMT. A third RMT, involving Pringles, fell apart because the proposed buyer turned out to have accounting problems. Ultimately, P&G sold Pringles to Kellogg for $2.7 billion in cash.

The Coty deal dwarfs those. P&G says it will show an after-tax profit of $5 billion to $7 billion for earnings purposes on the deal, which implies a pre-tax gain of $8 billion to $11 billion. We don’t know what the profit would be for tax purposes. If it were $5 billion, the tax savings are about $1.9 billion. If it’s $11 billion, about $4.2 billion.

The size of the gain depends on the price of Coty stock when the deal closes. When the deal was being negotiated, the price was $12.5 billion — 413 million shares of Coty, then worth about $10.6 billion, plus $1.9 billion in cash. But news leaked, Coty stock soared, and the deal was worth $15 billion when it was announced last week. At Coty’s closing price Friday, it was worth about $13.2 billion. The higher the price, the bigger P&G’s tax saving.

Look, if I were running P&G, I might well do Reverse Morris Trusts or the pending tax-free “cash-rich split-off” with Warren Buffett’s Berkshire Hathaway to swap its Duracell business and cash for Berkshire’s $4 billion-plus P&G stake. If you’ve got the right deal partners, it’s a lot easier to make money saving on taxes than by making your business bigger or more profitable. P&G’s three RMTs and Berkshire’s four cash-rich split-offs are bad public policy, but they’re well within the law.

If people get fed up with these deals, the way they did with excessive Morris Trust transactions in the 1990s, maybe our leaders will do something. You keep hoping. I’ll keep writing.