By John Letzing and David Enrich 

ZURICH--After seven years at the helm of Credit Suisse Group AG, outlasting the financial crisis and most of his fellow bank chief executives, Brady Dougan is known as a survivor.

He nearly lost that reputation.

As a yearslong U.S. tax-evasion investigation case was dragging on in recent months, board members at the giant Swiss bank mulled actions that likely would have cost Mr. Dougan his job, according to people familiar with the deliberations.

To expedite a legal settlement, Credit Suisse officials considered asking the Swiss government to implement an emergency law enabling the lender to sidestep bank-secrecy rules and hand over the names of certain clients to U.S. authorities, these people said. Board members believed such a request would mean Mr. Dougan would have to resign to appease Swiss politicians--something that seemed like a distinct possibility inside the bank until recently, they said.

Ultimately, Mr. Dougan, a 54-year-old Illinois native, dodged the bullet. Credit Suisse on Monday pleaded guilty in a Virginia court to aiding tax evasion and agreed to pay $2.6 billion to settle the case. Mr. Dougan remains in his job.

The turning point for Mr. Dougan apparently came earlier this month, when Switzerland's finance minister, Eveline Widmer-Schlumpf, flew to the U.S. to meet with U.S. Attorney General Eric Holder to discuss the investigation, said people familiar with the matter. After that meeting, the U.S. dropped its demands that Credit Suisse disclose its clients' names, these people said.

That allowed Credit Suisse to avoid having to appeal for emergency help to the Swiss Parliament, where some lawmakers have been calling for Mr. Dougan's head.

Nonetheless, as the size and severity of the tax-evasion settlement came into focus, Credit Suisse board members discussed whether they should make senior-management changes, according to people familiar with the board's discussions.

They ultimately concluded that Mr. Dougan, who joined a Credit Suisse predecessor in 1990, wasn't responsible for the criminal activity and that replacing him now would be too disruptive to justify any potential political benefits, these people said. Plus, some directors reckoned, it would be difficult to quickly find a suitable candidate to take over the country's second-biggest bank, one person said.

A Credit Suisse spokesman disputed the notion that board members discussed replacing Mr. Dougan, and said "the board backs the CEO."

On Tuesday, Mr. Dougan shrugged off questions during a conference call with analysts and reporters about whether he had felt pressured to resign. He said only that he had never considered stepping aside, adding that he's "committed to Credit Suisse."

Mr. Dougan is known as a soft-spoken Midwesterner who fits nicely into Zurich's relatively low-key financial community. He doesn't come off as overly slick. In a city of flashy cars, Mr. Dougan drives a Toyota Prius.

But he has sometimes rankled Swiss investors and politicians. He has faced criticism from local shareholders for failing to address them in German at the bank's annual meetings.

The biggest fracas came in June 2012. The Swiss National Bank stunned Credit Suisse executives by publicly questioning whether the bank was adequately capitalized. The comments, in the central bank's financial-stability report, knocked billions of dollars off Credit Suisse's market value.

Mr. Dougan angrily fired back, disputing the central bank's calculations and telling a Swiss newspaper that he found the SNB's position "difficult to comprehend." The extraordinary public spat triggered investor and media speculation about Mr. Dougan's grasp on the job.

Nearly two years later, though, Mr. Dougan remains CEO. "He is quite the survivor," said Canaccord analyst Arun Melmane.

Write to John Letzing at john.letzing@wsj.com and David Enrich at david.enrich@wsj.com

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