The number that participate in the government-brokered scheme is important for larger banks facing criminal investigations in the United States, such as Credit Suisse (>> Credit Suisse Group AG), Julius Baer (>> Julius Baer Gruppe AG) and Pictet & Cie.

These banks' talks with U.S. justice officials to settle their cases have been frozen pending a solution for the wider Swiss banking sector.

If the U.S. deems its deal with Switzerland a failure because too few banks come forward to make amends for aiding tax evasion, it is likely to hold up settlements for the larger banks.

The deal for second-tier banks, agreed in August, is part of a U.S. drive to lift the veil of Swiss bank secrecy which in 2009 led to UBS (>> UBS AG) paying $780 million in a settlement where the bank agreed to hand over U.S. client names with secret Swiss accounts.

Bank Coop (>> Bank Coop) and Migros Bank said on Tuesday they would participate in the U.S. scheme.

They join Valiant Holding (>> Valiant Holding AG) and Berner Kantonalbank (>> Berner Kantonalbank AG), two mainly retail banks, and Zurich-based private bank and securities firm Vontobel Holding AG (>> Vontobel Holding AG), which have also said they would take part.

Banks had until Monday to inform the Swiss regulator of their intentions.

Peter V. Kunz, professor of business law at Berne University, told Reuters on Tuesday he thought about 100 of the country's 300-plus private banks would participate.

The vast majority of Switzerland's private banks are not listed on the stock market, meaning they are under no obligation to publicly disclose how they plan to deal with the U.S. tax crackdown.

TOO RISKY

The U.S. scheme, which lapses at the year-end, requires banks to hand over some previously hidden information and face penalties of up to 50 percent of assets they managed on behalf of wealthy Americans. If the banks shun the offer, individual firms and senior staff risk criminal prosecution.

Coop, majority-owned by Basler Kantonalbank (>> Basler Kantonalbank AG) which is among the banks in the crosshairs of U.S. prosecutors, said staying out of the programme was too risky.

The bank took a 9 million Swiss franc ($10.14 million) provision and said it had only a few customers who were based in the United States, whose assets amounted to less than 0.3 percent of its total.

Migros said it was coming forward following comments from the Swiss regulator, which told banks they should err on the side of caution in judging their dealings with American clients.

($1 = 0.8874 Swiss francs)

(Reporting by Caroline Copley and Katharina Bart; Editing by Erica Billingham)