In August 2012, Hillary Clinton became the first secretary of state to visit the islands. Her public remarks on the main island, Rarotonga, did not contain a word about the trusts. A Congressional Research Service study on tax havens released in January cited offshore trusts, in the Cooks and elsewhere, as possible conduits for evading taxes, with little follow-up.

“There’s been a lot of pressure on the Caymans and other places to clean up,” said Heather Lowe, director of government affairs at Global Financial Integrity, a Washington research and advocacy group. “There are many areas where pressure is not exerted, and the Cooks is one of them. Using a Cook trust to hide assets from your spouse may not make the headlines.”

Given the Cooks’ success in attracting money, a number of other countries — about 25 and growing — and about 14 states have developed some form of asset protection law. In the United States, the first was Alaska, which enacted an asset protection statute in 1997. Delaware followed, along with South Dakota, Nevada, Wyoming and others. Many domestic trusts, however, have been broken open — “pierced,” in legal parlance — allowing creditors who win judgments to tap into the assets. Most other countries’ asset protection laws are not considered as tough as those of the Cooks.

For the islands, the trust business has been a bonanza. The Cooks have a stable government and a sophisticated judiciary based in English common law. Business generated by the trusts — registration fees, taxes on trust companies and their employees, and various support services — accounts for just above 8 percent of the $300 million Cooks economy, after tourism and ahead of fishing. Cash and investment accounts, along with real estate and businesses, are typically registered in the trusts. None of the items have to be physically located in the Cooks, and business can be conducted electronically.

The Cooks law was written with Americans in mind. In fact, it was drafted by a Denver lawyer, Barry Engel. A Cook official, seeking revenue for the islands, read in The Economist about Mr. Engel’s firm, which was pioneering the concept of asset protection trusts, and hired Mr. Engel to help write the 1989 law.

“Lawyers can debate the morality of these trusts,” said Mr. Engel, who has established more than 1,300 Cook trusts. “My first duty is to my clients and my clients have a need. This is in response to a legal system that has spun a little out of control and is abused by lawyers for legal extortion and who can throw someone’s life into a tailspin. Trusts are our response to that abuse of the legal system.”