Wealthy tax evaders with assets stashed offshore can come clean with U.S. authorities under a new amnesty program with reduced penalties, the government said Tuesday.

“It gives people a chance to come in before we find them,” Internal Revenue Service Commissioner Doug Shulman said. The new effort follows a 2009 amnesty program, which lured 15,000 taxpayers with hidden accounts.

It is unclear whether this effort will net as many wealthy tax cheats as the prior one, which was backed by the force of the U.S. government’s fraud case against UBS AG , alleging the Swiss bank helped U.S. citizens avoid taxes.

Publicity surrounding the government’s case against UBS, and fears among the bank’s U.S. clients that their names could end up in government hands, spurred an unprecedented response to the earlier amnesty, tax attorneys said.

However, this fresh effort could help the U.S. government gather more information into other international banks suspected of helping Americans evade the IRS.

Shulman said a “number of other banks” were under investigation, with some cases at “quite advanced” stages. He declined to name them.

The government has closed 2,000 cases from its initial set of disclosures, bringing in $400 million to government coffers. That program carried a 20 percent penalty.

“As we continue to amass more information and pursue more people internationally, the risk to those hiding assets offshore is clearly increasing,” Shulman said.

Under the new program, participants face a 25 percent penalty for the year with the highest balance, compared with the usual penalty of 50 percent for each year.

“This number is about the best we could have expected in terms of the percentage,” said former IRS official Mark Matthews, now a tax lawyer for wealthy individuals.

Several lawyers noted several steeper hurdles in the new program, including collection of eight years of tax records compared to an earlier six years.

“I don’t believe we will see the wave we saw in 2009 because the threat of exposure is not as direct,” said Barbara Kaplan, a tax lawyer in New York City.

UBS settled the U.S. government’s fraud case against it in 2009 by paying $780 million and agreeing to hand over the names of hundred of clients. A related civil suit was settled last year on condition Swiss authorities reveal thousands of names.

Prosecution of another bank “would be a hammer,” to bring more individuals in, Kaplan said.

Shulman declined to say whether the government would use the same strategy as it did with UBS — employing what is called a “John Doe” summons against the bank.

“They are at various stages but some of them are quite advanced,” Shulman said of the other bank probes.

Such a summons describes the types of clients at the bank based on their actions but without specific names.

Last year, the Department of Justice notified clients of HSBC  that they are targets of a criminal probe. HSBC has maintained it is fully compliant with the law.

Under the new amnesty program, taxpayers whose accounts or assets total less than $75,000 in a calendar year may pay a penalty of 12.5 percent.

The closing date is Aug. 31.