Mr. Finzer, an American based in Novi Sad, Serbia, advertises his services online. “Tax-Free Havens for Non-U.S. Citizens,” his Web site, says. It goes on: “More than 50 percent of the major corporations in the world are incorporated in Delaware. Why? Because in provides the anonymity that most offshore jurisdictions do not offer.”

That is exactly what troubles law enforcement agencies and some in Congress who are trying to rein in Delaware. The state is seen as an onshore alternative with regulations more lax than such well-known offshore tax havens as the Isle of Man, Jersey and the Caymans, which require greater disclosure. Even more, a Delaware registration allows a business, legitimate or not, to open a bank account anywhere in the world with the patina of an American address.

“You can have companies in Delaware that have no U.S. bank accounts, no requirements for documentation and no one knows who owns them,” says Anthony B. Travers, chairman of the Cayman Islands Stock Exchange and former chairman of that country’s Financial Services Association. “There should be a level playing field and Delaware should have to comply with the same standards as the Caymans.”

Delaware isn’t the only state that has gone this route. Three others — Nevada, Wyoming and Oregon — have also been cited by the Financial Crimes Enforcement Network, a division of the United States Treasury Department, as “particularly appealing” for the formation of shell companies. Of those four states, Delaware stands out as the one offering the least transparency and the most secrecy, this group says.

“What is so galling about secrecy in the United States is that there is no attempt to document who owns a corporation,” said Richard Murphy, a senior adviser at the Tax Justice Network, an independent organization based in London that researches tax havens. “Two million corporations are formed each year in the United States, more than anywhere else in the world. Delaware, in turn, is the biggest single source of anonymous corporations in the world.”

Mr. Murphy adds: “Why go to the Caymans when you can just go down the street?”

In 2009, the Tax Justice Network named the United States as No. 1 on its Financial Secrecy Index, ahead of Luxembourg and Switzerland. It cited Delaware as one of the reasons.