Some Swiss banks and other financial firms are offering to compensate U.S. clients who had undeclared accounts in the past if they confess them to the Internal Revenue Service. By doing this, the banks can reduce their own penalties for having encouraged U.S. tax evasion.

Americans who accept these offers may still owe large sums to the IRS, however, say a sampling of advisers familiar with the proposals.

The Swiss firms are typically offering to pay clients a few thousand dollars, and no more than $5,000, advisers say.

That may not make much of a dent in the taxpayer’s penalty on undisclosed accounts. For taxpayers accepted into the IRS’s limited-amnesty program, that penalty is now 27.5% of the account’s highest balance.

Such a penalty may seem stiff, but the law allows fines of up to 50% per year, per account if the taxpayer isn’t in the IRS’s limited-amnesty program. In a recent civil court case (U.S. v. Zwerner), the taxpayer was required to pay a penalty that equaled or exceeded the total amount in his secret Swiss account.

The Swiss firms can’t lessen their own penalties, and hence won’t be offering payments, unless the client confessed to the IRS after the bank sent a warning letter. Because many banks sent multiple warning letters, confessions often occurred after the account holder received at least one letter, advisers say.

But if the client stepped forward before receiving such a letter — say, in response to reading a news article about UBS UBS, -1.95% — then the client’s confession to Uncle Sam can’t be used to lessen the bank’s own penalty.

Some U.S. account holders are accepting the offers of reimbursement, advisers say, especially if they are only now stepping forward to the IRS. “It helps take the sting out of a confession,” says one adviser.

An expanded version of this report appears at WSJ.com.

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