LIKE MOST SWISS, CHRISTOPH MÜLLER NEVER PAID MUCH heed to the doings of the country’s high-flying bankers. The 40-year-old Müller regularly puts in 13-hour days running his construction supplies company in Langenthal, a small town some 25 miles northeast of the capital of Bern, and he assumed that the big banks managed themselves at least as sensibly as he and his fellow small-business owners managed their concerns. So when giant UBS ran up Sf21.3 billion ($23.8 billion) in losses on U.S. subprime securities in 2008 and needed a Sf43 billion taxpayer bailout, he was understandably livid. “In the old days, if a banker lost that much money, he would jump out a window,” says Müller.

The Swiss may not be storming Zurich’s Paradeplatz to demand the defenestration of bankers, but Müller is far from alone in his anger. The losses at UBS broke a bond of trust between Switzerland’s big banks and its citizens, an extraordinary development in a country where banking is as much a part of the national identity as watchmaking and chocolate. Suddenly, it’s no longer safe to assume that what’s good for Credit Suisse and UBS is good for Switzerland. The financial crisis demonstrated that problems at those big banks — whose combined assets are four times the size of the national economy — could overwhelm government resources just as the banking blowups in Iceland and Ireland had.

The government and Swiss regulators have responded with the most radical overhaul of banking rules in the industrial world, one....