WASHINGTON– Mitt Romney’s former private equity firm used a half-dozen companies and partnerships in the tax havens of Luxembourg, Ireland and the Grand Caymans four years ago to channel $689 million in loans to a U.S. company that it co-owned. To the average American, the deal might seem bizarre.

But some tax experts say that the circuitous paper chain likely was structured to avoid certain taxes for passive investors, including blind trusts for the Republican presidential candidate and his wife.

It’s just one of a maze of transactions involving the Romney family portfolio that were engineered in tax-neutral nations.

The gradual emergence of outlines of these deals in recent weeks is prompting some experts to challenge Romney’s pronouncement that his scores of offshore investments haven’t lowered his federal taxes by so much as a dollar.

“It appears likely that offshore entities helped his investments avoid taxes or adverse tax consequences,” David Miller, a prominent New York tax attorney, told McClatchy Newspapers.

The New York Times reported Tuesday that it obtained documents showing that an offshore fund in which Romney’s investment retirement account held an interest probably used a “blocker” an intermediary company that legally insulated the White House hopeful from paying 35 percent in taxes.

The release of documents from entities set up by Bain Capital Inc., the firm that Romney ran from 1984 to 1999, also are lifting a shroud from the dizzying world of private equity.

This is an industry that has racked up huge profits with help from a small army of tax attorneys.

Critics say these firms have found ways to exploit gaps between U.S. and other countries’ laws to deprive the U.S. treasury of billions, if not tens of billions, of dollars.

The offshore deals are generally considered legal, typically structured to shield pension funds, foundations and other tax-exempt organizations from U.S. taxes, and foreign investors from U.S. taxes or taxes in their own countries.

The California State Teachers’ Retirement System, for example, has since 2006 invested more than $500 million in three of the funds in which Ann Romney’s trust holds a stake.Bain said in a statement that it must navigate complicated international tax treaties and tax codes for its clients.

“So, like virtually all global asset managers, we use widely accepted, fully legal and recognized structures so that investors may receive predictable tax treatment on investment gains for their constituents,” the statement said.

Even indirectly, Romney benefited. Whenever Bain’s strategies reduced taxes for a fund, he reaped returns because his 10-year retirement package gave him a slice of the management fees and profits from Bain Capital deals.

The lower the taxes, the bigger the returns for each partner.

Because of the secrecy surrounding tax filings, no hard proof has surfaced that the Romneys actually realized any tax breaks from their offshore dealings.

Such opaque rules leave tax experts making educated guesses.

Romney, whose tenure as Bain Capital’s chief executive helped him amass a fortune worth up to $250 million, has refused to release enough financial data to definitively settle the touchy question of whether he got offshore tax reductions.

The issue of how much he’s paid in taxes while piling up all of that money and his refusal to release more than two years of his personal tax returns have dogged him for months and could come up Wednesday night when Romney meets President Barack Obama in the first of three presidential campaign debates.

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Miller, the tax lawyer, has reviewed Romney’s 2011 tax return and evaluated what’s public about some of the offshore deals. He’s found several instances in which evidence suggests Romney got tax breaks, including for his individual retirement account.

Miller’s assessment is at odds with Romney’s campaign. Michele Davis, a spokeswoman, said in a statement that “investments by the blind trusts in funds established outside the U.S. are taxed in the very same way they would be if the shares were held in the U.S.”

“No taxes are evaded or reduced,” Davis said. “These funds are all registered with the IRS (Internal Revenue Service) and report all income to investors and the IRS, just like domestic funds.”

By definition, private equity funds have few public reporting requirements, so obtaining financial statements from some of the offshore companies doesn’t definitively reveal what taxes might have been avoided.

Details of the Romneys’ offshore investments are evidenced in the couple’s recently released 2011 tax returns, the GOP presidential nominee’s financial disclosure statements, a trove of internal Bain documents posted by the Internet site Gawker.com, and filings in Luxembourg and Ireland obtained by McClatchy.

• Greg Gordan, MCT Campus