The Internal Revenue Service is giving the wealthy yet another chance to voluntarily come clean about the money they’re hiding offshore.

On Monday, the IRS reopened its Offshore Voluntary Disclosure Program (OVDP) to aid those hiding offshore accounts get current with their taxes, and reported the collection of more than $4.4 billion so far from the two previous international programs it held in 2011 and 2009. 

The IRS says that the third offshore program comes as the IRS “continues working on a wide range of international tax issues and follows ongoing efforts with the Justice Department to pursue criminal prosecution of international tax evasion.”

The OVDP will be open for an “indefinite period,” the IRS says, until it announces otherwise.

IRS Commissioner Doug Shulman said in a statement announcing the third OVDP that the IRS’ focus on offshore tax evasion “continues to produce strong, substantial results for the nation’s taxpayers.” The IRS, he said, has “billions of dollars in hand from our previous efforts, and we have more people wanting to come in and get right with the government. This new program makes good sense for taxpayers still hiding assets overseas and for the nation’s tax system.”

The third installment of the program is similar to the 2011 program, but with a few key differences. Unlike last year, there is no set deadline for people to apply, but the terms of the program could change at any time, the IRS says. For example, the IRS may increase penalties in the program for all or some taxpayers or defined classes of taxpayers-–or decide to end the program at any point.

“As we’ve said all along, people need to come in and get right with us before we find you,” Shulman said. “We are following more leads and the risk for people who do not come in continues to increase.”

The IRS has collected $3.4 billion so far from people who participated in the 2009 offshore program, reflecting what the IRS says are closures of about 95% of the cases from the 2009 program. The IRS has also collected an additional $1 billion from up-front payments required under the 2011 program. “That number will grow as the IRS processes the 2011 cases,” the IRS says.

In all, the IRS says that it has seen 33,000 voluntary disclosures from the 2009 and 2011 offshore initiatives. “Since the 2011 program closed last September, hundreds of taxpayers have come forward to make voluntary disclosures. Those who have come in since the 2011 program closed last year will be able to be treated under the provisions of the new OVDP program,” the IRS states.

The overall penalty structure for the new program is the same as it was for 2011, except for taxpayers in the highest penalty category.

For the new program, the IRS explains that the penalty framework requires individuals to pay a penalty of 27.5% of the highest aggregate balance in foreign bank accounts/entities or value of foreign assets during the eight full tax years prior to the disclosure. That is up from 25% in the 2011 program. Some taxpayers will be eligible for 5% or 12.5% penalties; these remain the same in the new program as in 2011.

Participants must file all original and amended tax returns and include payment for back-taxes and interest for up to eight years as well as paying accuracy-related and/or delinquency penalties.

Participants face a 27.5% penalty, but taxpayers in limited situations can qualify for a 5% penalty.

Smaller offshore accounts–those with offshore accounts or assets that did not surpass $75,000 in any calendar year covered by the new OVDP–will face a 12.5% penalty. As under the prior programs, taxpayers who feel that the penalty is disproportionate may opt instead to be examined.

The IRS also says that it is developing procedures for dual citizens and others who may be delinquent in filing, but owe no U.S. tax taxpayers may come into compliance with U.S. tax law.