The walls of Swiss bank secrecy came tumbling down Wednesday when UBS agreed to pay $780 million in fines to settle tax-fraud charges—and, significantly, to hand over the names of Americans who had parked money in Switzerland to evade hundreds of millions of dollars U.S. taxes.

Exactly how many names are coming remains to be seen. Estimates range from a few hundred to several thousand clients.

The Wall Street Journal and Financial Times put the number at 250. The Neue Zuricher Zeitung said it could approach 300 clients.

The New York Times and Associated Press say the number could eventually approach 17,000 or even 19,000 people, based on earlier assertions by federal authorities.

A list of the clients was included in the 18-page deferred prosecution agreement UBS struck with the U.S. Justice Department, but that list was sealed by the U.S. District Court in Fort Lauderdale, Florida.

The names are scheduled to be released when the federal district court accepts the agreement. That could be as soon as Thursday.

In the past, prosecutors have said that UBS helped Americans hide $20 billion in assets and thus avoid $300 million a year in taxes from late 2002 through 2007.

UBS faced a difficult task in answering the federal allegations that its bankers deliberately marketed Swiss bank secrecy to U.S. clients who were interested in evading income taxes in this country.

In 2004 alone, for example, about 32 UBS bankers traveled to the U.S. to meet with American clients nearly 3,800 times to discuss their clients’ Swiss bank accounts, according to court documents. The government said that UBS bankers tried to hide their business by using code words, encrypted laptops, and "other counter-surveillance techniques."