On the same day that Mitt Romney cracked his birther “joke,” new evidence indicated that he and his partners at Bain Capital have used questionable methods to avoid federal taxes — including a scheme that transforms corporate stock into untaxed offshore “derivatives” and a practice that converts management fees into capital gains, which are taxed at a far lower rate.

While nobody has asked to see the Republican candidate's birth certificate, as he said at a Michigan rally on Friday, everybody has a renewed interest in examining the tax returns he continues to withhold.

The complex and tricky tax shelters used by Bain Capital continued to emerge as lawyers and other experts examined the hundreds of pages of previously confidential company documents uncovered by the Gawker website in an exclusive series this week. The authenticity of the documents was confirmed by a Bain spokesperson, who said that the company deplores the public posting of its proprietary materials.

In a sense, the latest revelations about how Bain protected its vast income from taxation are scarcely surprising to anyone familiar with the world of private equity where Romney made his fortune, estimated at $250 million or more. Avoiding taxes is among the most important attractions of that industry for the wealthy clients it aims to attract.

But several experts who have looked over the new Bain documents have warned that dubious legal tactics may have been employed by some of the company's investment vehicles, including several that are listed on the partial returns that Romney has already released. Those experts, such as Victor Fleischer, a law professor at the University of Colorado, and Daniel Shaviro, who teaches tax law at New York University's law school, have raised questions about both the equity "swap" and fee-conversion maneuvers.

Companies like Bain make money both from investment income, which is taxed at the lower capital gains rate, and from management fees, which are taxed as ordinary income like wages.

If the firm can somehow transform its management fees into capital investments, then it can avoid the 35 percent top federal income tax rate and pay the 15 percent capital gains rate, instead.

That is what Bain evidently does to keep its partners' taxes low — around the 13 percent rate that Romney admits to paying. But critics like Fleischer say this is an abusive tactic that cannot be justified by law, even though the IRS has never attempted to stop companies that use it.

"Unlike carried interest, which is unseemly but perfectly legal, Bain's management fee conversions are not legal," the Colorado professor wrote on his blog. "If challenged in court, Bain would lose. The Bain partners, in my opinion, misreported their income if they reported these converted fees as capital gain instead of ordinary income."

Equally troubling is the use of offshore accounts to avoid taxation on stock holdings. This tactic is called a "total return equity swap," because it involves swapping real equities for derivative paper investments that provide all the same dividends as the stock itself — but aren't subject to federal taxes. According to Shaviro, this practice was sufficiently blatant to elicit a warning from the IRS two years ago. He wrote recently that those who used it over the past decade "were coming perilously close to committing tax fraud, in cases where the economic equivalence to direct (stock) ownership was too great."

In the complex territory of tax law, precise boundaries aren't always clear. What makes the "total return equity swap" potentially perilous for Romney, however, is the use of foreign accounts to avoid taxes, which is what many Americans suspect him of doing. Despite the accounts that he has maintained in Switzerland, the Cayman Islands, Luxembourg, Bermuda and other tax havens, Romney's campaign has repeatedly denied, with little credibility, that his wealth was invested abroad to evade taxes.

The proof may well lie within the tax returns that he is so determined to conceal. Wisecracks about the president's alleged foreign birthplace may not distract concerned voters from the overseas accounts where Romney's money has been hidden.