WASHINGTON – The Internal Revenue Service has recouped more than $5.5 billion under a series of programs that offered reduced penalties and no jail time to people who voluntarily disclosed assets they were hiding overseas, government investigators said Friday.

In all, more than 39,000 tax cheats have come clean.

But there’s more.

Government investigators suspect that thousands of other taxpayers have quietly started reporting foreign accounts without paying any penalties or interest. The number of people reporting foreign accounts to the IRS nearly doubled from 2007 to 2010, to 516,000 accounts, a report by the Government Accountability Office said.

The sharp increase suggests that some people are simply starting to report their accounts without taking part in the disclosure programs, the report said.

“IRS has detected some taxpayers with previously undisclosed offshore accounts attempting to circumvent paying the taxes, interest and penalties that would otherwise be owed,” the report said. “But based on GAO reviews of IRS data, IRS may be missing attempts by other taxpayers attempting to do so.”

Some taxpayers try to avoid penalties through a technique the IRS calls “quiet disclosure,” in which they file amended tax returns that report offshore income from prior years. Others simply declare existing offshore accounts for the first time with their current year’s tax return, the report said.

“If successful, these techniques result in lost revenue for the Treasury and undermine the offshore programs’ fairness and effectiveness,” the report said.

Peter Zeidenberg, a partner at the law firm DLA Piper in Washington, said it’s pretty obvious that people are starting to report foreign accounts that probably existed for years.

“I don’t think you get an increase like that from people just all of a sudden getting the idea I’m going to open an account in Switzerland,” Zeidenberg said.

Acting IRS Commissioner Steven Miller said catching overseas tax dodgers is a top priority of the agency. In a written response to the report, he said the agency is working to improve the way it identifies people who are still trying get around the disclosure programs.

The IRS has run four voluntary disclosure programs since 2003. The last three — in 2009, 2011 and 2012 — have yielded almost all of the $5.5 billion in back taxes, penalties and interest. The latest program is still open.

The agency stepped up its efforts in 2009, when Swiss banking giant UBS AG agreed to pay a $780 million fine and turn over details on thousands of accounts suspected of holding undeclared assets from U.S. customers.

The GAO’s report looked at data from the 2009 program. More than 10,000 cases from that program have been closed so far. The median account balance: $570,000.

U.S. taxpayers can hold offshore accounts for a number of legitimate reasons, the report says. They may want to diversify their investments, facilitate international business transactions or get easier access to money while living or working overseas.

But “some use them to illegally reduce their tax liabilities, often by not reporting the income earned on these accounts.”