The Internal Revenue Service announced it is reopening its limited amnesty program for U.S. taxpayers with undeclared foreign accounts, and it also presented further results from the first two programs in 2009 and 2011.

IRS Commissioner Doug Shulman that more than 33,000 people stepped forward for the first two programs, and so far the agency has collected more than $4.4 billion from them. We calculate that's an average of $133,000 per case, but Shulman said he expects the revenue to grow as more cases are closed.

He...