(FORTUNE Magazine) – When President Bush announced last December that William Donaldson was his choice to replace Harvey Pitt as chairman of the Securities and Exchange Commission, the reaction was generally positive. Pitt had been a bumbler, unable to address the very significant problems faced by the SEC, while Donaldson, 71, seemed a rock-solid choice with an impeccable resume: class of 1953 at Yale (where, like Bush, he belonged to the Skull and Bones secret society), founder of the Wall Street firm Donaldson Lufkin & Jenrette (bought in 2000 by CSFB), founding dean of the Yale School of Management, a former head of the New York Stock Exchange, and CEO of Aetna.

And yet behind Donaldson's glossy CV there are questions about how much he accomplished in those various positions. Is he the strong leader the troubled SEC so desperately needs? Or is he a caretaker, a man whose establishment connections have enabled him to "fail up," as one Wall Street executive put it? People in the financial community say there are many better-qualified candidates, including Harvey Goldschmid, an SEC commissioner; John Biggs, the former head of TIAA-CREF; and Peter Fisher, undersecretary of the treasury.

Donaldson has some heavyweight defenders. "I have a very high regard for him," says Hank Paulson, CEO of Goldman Sachs. Donaldson also has a number of detractors, most of whom were reluctant to speak for attribution for fear of offending such a power broker. However, even the critics acknowledge that Donaldson deserves credit for building DLJ into a significant player on Wall Street. DLJ was the first Wall Street firm to focus on research, and it was also the first to go public. (Old-time DLJers like to tell of how, in the early days, each of the founders chose an animal that he thought best represented himself. Lufkin chose a fox, Jenrette a bear, and Donaldson an eel. Go figure!)

Donaldson's post-DLJ career is less impressive. In October 1973 he went to Washington to become Henry Kissinger's undersecretary of state for security assistance. He left after only seven months. Kissinger told FORTUNE that Donaldson was "frustrated [by the] complex bureaucratic situation." Others say he washed out.

In 1975, Donaldson became dean of the brand-new Yale School of Management. SOM, as it is called, was supposed to be a new kind of graduate business school that would rival Harvard in quality yet would focus more on issues of management. "At Yale we believe that understanding...and implementing positive change in this century and beyond will require a new kind of manager and a new kind of managerial education," Donaldson said at the time. But when he left Yale after five years, the business school had not fulfilled its promise. Although SOM later changed its curriculum to match those of more traditional business schools, it has never attained the stellar reputation of Harvard, Stanford, or Wharton.

Donaldson, who declined to talk to FORTUNE on the record, then opened his own investment firm, Donaldson Enterprises. FORTUNE has learned that it ran an offshore fund incorporated in the Cayman Islands. The principal reason for setting up an offshore fund, of course, is to minimize regulatory oversight and taxation by the U.S. government. Donaldson raised $100 million for the fund in the early 1980s, mostly from foreign investors. Despite the bull market, it was not a success, and he ended up returning the investors' money.

In 1991, Donaldson became chairman of the New York Stock Exchange, where critics complained that he was ineffectual. "He didn't do anything I know about to prepare the NYSE for the future," William Freund, the NYSE's former chief economist, told Bloomberg News. Ironically, Donaldson clashed with SEC chief Richard Breeden--who had been appointed by the first President Bush--over the listing of foreign corporations. Donaldson argued that they should be able to list on the NYSE with less financial disclosure. In that same vein Donaldson also derided Regulation Fair Disclosure in an October 2001 article in Institutional Investor, saying the new law was "crazy in terms of what it does to the free flow of information...it's a terrible rule."

Donaldson's latest stop was at insurance giant Aetna, where he had been a board member. When he became CEO in February 2000, the company was tottering, and under attack for payment and treatment practices that lawyers alleged were illegal. Donaldson stabilized the situation by slashing costs and wooing unhappy doctors. But he left after 14 months, having collected $20 million in cash, stock, and options.

FORTUNE has also learned that there are issues in Donaldson's personal life. In 1960 he married a woman named Evan Burger. They lived in Manhattan and adopted two children, now grown. Sources say that at some point in the 1980s, Donaldson became romantically involved with a married woman named Jane Morrison, who worked at the Yale School of Management when Donaldson was dean. She was the wife of Bruce Morrison, then a Democratic Congressman from Connecticut. Twelve years ago, while Donaldson was still married to Evan, Jane Morrison gave birth to a child by Donaldson. (Newspaper reports say that Jane and Bruce Morrison divorced in April 1990 after having been separated for two years.)

On April 30, 1994, Evan died unexpectedly of a cerebral hemorrhage. In late December 1995, Donaldson married Morrison. Sources say the FBI has known about Donaldson's affair and child since he was nominated in December. So, too, has the White House. Although the Bush administration has strongly promoted its commitment to family values and moral rectitude, a White House spokesperson says, "The President believes that Bill Donaldson would make an outstanding SEC chairman." Some longtime Donaldson associates seem less sure. "This kind of behavior calls his character into question," says one. "And character is an important thing for the next head of the SEC to have."

The Senate Banking Committee will begin Donaldson's confirmation hearing on Feb. 5. Questions about his professional accomplishments will be front and center. It remains to be seen whether his private life will also become an issue.