The plan was developed amid a widening investigation into American clients of UBS but will apply to clients of other banks.

Under the plan, the I.R.S. will cut a penalty for not filing a Report of Foreign Bank and Financial Account, known as an Fbar  something offshore tax evaders have not done, to avoid detection by the I.R.S.

The current penalty is up to 50 percent of the highest annual balance of each account for each of the last three years  an amount that can quickly wipe out an investor and still leave him owing taxes and interest. While the number of Americans coming forward this year to disclose hidden assets has doubled, the I.R.S. said, it is still not enough.

Now, the I.R.S. will reduce that penalty to 5 to 20 percent, depending in part on whether the wealth was inherited. It will also levy the penalty just once, on the highest balance in the accounts over the last six years.

Still, with many accounts holding securities that have plunged in value because of faltering stock markets, the new lowered penalty will still have some sting.