Executives at Swiss banks Julius Baer and Credit Suisse expect to avoid a U.S. tax investigation into their private banking businesses on the same scale as their peer UBS , they told The Financial Times on Sunday.

UBS, Switzerland's No. 1 private bank, earlier this month agreed to reveal the names of thousands of UBS's rich U.S. clients to Washington to settle a tax-avoidance dispute seen as threatening Swiss banking secrecy.

But the agreement leaves the door open for similar actions against other banks, the newspaper said, adding that criteria for follow-up actions have not been disclosed.

But Boris Collardi, chief executive of Julius Baer, told the newspaper his bank is prepared. There may be some requests for information (from tax authorities), but I don't think we face the risk of another John Doe summons, he told the FT.

Credit Suisse Private Banking head Walter Berchtold said the bank had taken measures and established clear rules for its business. From that point of view, I'm very comfortable, he said in an interview with the newspaper.

Switzerland's private banks manage an estimated $2 trillion of foreign wealth.

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