The end of a limited-amnesty deal isn't expected to stop Americans with secret Swiss bank accounts from coming in from the cold. They may just find the reception a little chillier.

A program offering more-lenient terms, including less chance of criminal prosecution, lured in 7,500 account holders before it ended on Thursday. But a longstanding Internal Revenue Service program for people who turn themselves in remains in place.

Thousands of account holders who didn't take advantage of the IRS deal will probably get letters from UBS AG warning them that they could be in the agency's sights; their names are being provided by Switzerland to U.S. tax authorities under a tax-evasion settlement between the countries with the Justice Department. Even if they fight disclosure in Swiss courts, their records almost certainly would be turned over to the IRS, say tax lawyers.

"Realistically, they have no choice but to make a voluntary disclosure before that happens or they run a serious risk of criminal prosecution and jail," says Scott D. Michel, an attorney at Caplin & Drysdale in Washington, D.C.

Still, some people are likely to try to stay under the radar, says Dean Zerbe, a lawyer representing former UBS banker Bradley Birkenfeld in his whistleblower claim at the IRS. "The real bad actors -- the big fish -- they are definitely going to keep at it and hope the IRS doesn't find them," he says.

For those who decide to come clean, making a disclosure now is akin to diving into uncertain waters, as the IRS will have wide leeway in imposing penalties. Mr. Michel says he hopes the IRS will supply new guidance, so people know what they may be facing.

Edward M. Robbins Jr., a partner at the law firm Hochman Salkin Rettig Toscher & Perez in Beverly Hills, Calif., says account holders can expect to "see their civil price tag go up." At a minimum, he says, they could lose as much as 20% or more of their savings just for failing to file a standard Report of Foreign Bank and Financial Accounts. In a worst-case scenario, he says, they could lose half the account value.

Among those who turned themselves in before Thursday, accounts ranged in size from just above $10,000 to more than $100 million and were in several hundred banks in 70 countries, according to the IRS.

The IRS remains willing to work with any taxpayer who wants to come forward and make a voluntary disclosure, even though the special program is over, says agency spokeswoman Michelle Eldridge.