UPDATE 1-NYSE head cautious on 'Shareholder Bill of Rights'

* Duncan Niederauer says bill might not fit smaller firms

* Bill would give shareholders influence over boards

NEW YORK, June 9 (Reuters) - The head of New York Stock Exchange parent NYSE Euronext (NYX.PA)(NYX.N) said on Tuesday there is room for compromise in proposed U.S. legislation that would give shareholders more influence over executive pay and the composition of boards of directors.

It is reasonable to demand changes in the boardrooms of companies "whose lack of risk management could impact adversely systemic risk in the United States and beyond," said Duncan Niederauer, chief executive of the world's largest exchange operator, measured by the size of listings.

But "a lot of what is in that bill is not flexible enough," he told a meeting of New York's Japan Society. "It's not about creating loopholes, it's just that some of the rules don't make a lot of sense when applied to a small company."

Democratic Sen. Charles Schumer last week introduced a bill in the U.S. Senate, called the "Shareholder Bill of Rights," that would give shareholders a "say on pay" and a voice in the corporate boardroom.

Niederauer said that while some companies may need to adopt risk committees and split the role of chairman and CEO, such steps may not be appropriate for smaller firms.

"I want that person to be responsible and accountable in both ways," he said of the heads of some smaller firms listed on the Big Board.

"There's lots of room for compromise in there, and I think a lot of our companies are feeling the same way," he said. (Reporting by Jonathan Spicer; editing by John Wallace)