Stock market operations were not affected by the resignation of chairman Richard Grasso under pressure over his $140 million salary package. But many Wall Street players are rethinking how the New York Stock Exchange should be managed.

At the New York Stock Exchange, the line between regulation and profit-making has often blurred, especially in recent months, allowing many conflicts of interest to arise.

For instance, Mr. Grasso became a board member of several companies that traded shares on the New York Stock Exchange, where he was serving as chairman in charge of regulatory practices. And in March, the chairman of Citigroup, Sanford Weill, was nominated to become a member of the New York Stock Exchange board, after his company agreed to pay out $400 million in a settlement between regulators and brokerage firms. He later withdrew his nomination under scrutiny.

Paul Lapides, head of the Corporate Governance Center at Kennesaw State University near Atlanta, Georgia, says these questionable practices must change.

"It just made no sense, the argument that Dick Grasso and some of the others at the Exchange would learn something from sitting on [boards of] companies that they were overseeing and regulating," he said. "It is absolute nonsense. They can sit on NASDAQ companies."

Separating regulatory practices from trading operations may become a top priority for the Securities and Exchange Commission, the federal agency in charge of reviewing governance standards.

Mercer Bullard, head of Fund Democracy, an investor advocate group, says the New York Stock Exchange should learn from the leadership model of the National Association of Securities Dealers, which operates the NASDAQ market.

"I would go to the NASD model and look for a big name to oversee what would be a split set of responsibilities, and then leave it to the members of the NYSE to find the best person for the operations side," he said.

Changes are expected within the 26-member board of the New York Stock Exchange, the very group that approved Mr. Grasso's controversial salary package. Some are saying the board must be held accountable.

Bernard Marcus, a former head of the NYSE board's compensation committee, is among those calling for the entire board to resign.

"I think that, first of all, all of those people who voted for this compensation and then asked him to leave, I think they should leave the board," he said. "I think they do not deserve to be on this New York Stock Exchange board. And myself, as a private investor today, I feel very uncomfortable about them."

Mr. Grasso is credited with getting the Stock Exchange up and working within days of the September 11, 2001, attacks on New York, and a rare ability to balance traditional stock trading and new technology.

With so many structural questions yet to be resolved, the right person for the vacant chairman's post has not been easy to find. Board member Larry Sonsini was offered the position of interim chair, but did not accept. Amid speculation that former Treasury Secretary Robert Rubin might be a candidate, Mr. Rubin promptly announced his disinterest in the post.

Mr. Grasso's $140 million salary was revealed when new governance regulations required that such figures be released. Muriel Siebert, the first female member of the New York Stock Exchange, says more should be done to open the process to the public.

"We should have transparency," she said. "The board of the NYSE should say how is the stock exchange going to function. They should have some open hearings. They should get the SEC [Security and Exchange Commission] involved. They should get some institutional investors involved, some individual investors involved. And then say, 'Should not we restructure this board? Should not we have more outside independent directors than we have industry directors?'"

Restructuring the market and opening it to greater public scrutiny may be a long and contentious process, especially because the furor over Mr. Grasso's compensation comes in the wake of a series of highly publicized corporate scandals.