The head of the New York Federal Reserve Bank says that banks must improve their culture. Banks must change the way employees are compensated and take other steps to fix a corporate culture that encourages misdeeds or face being broken up, said William C. Dudley.

If bad behavior persists, “the inevitable conclusion will be reached that your firms are too big and complex to manage effectively,” Dudley said.

Dudley’s comments, which follow bank scandals involving Libor and foreign exchange trading, were made at a closed-doors workshop attended by senior bankers at the New York Fed on reforming Wall Street culture and behavior.

Lawmakers have enacted a major overhaul of the rules designed to prevent banks becoming “too big to fail.” Dudley said it was fair to question if the “sheer size, complexity and global scope of large financial firms today have left them ‘too big to manage.’”

Dudley, who has had to defend the New York Fed recently against allegations it was too soft on big Wall Street firms, suggested a number of ways to better align bank employee incentives with the interests of the general public.  These include deferred compensation plans that switch emphasis to debt, rather than equity, and a centralized, industry-wide registry for tracking individual offenses.

Fines levied against banks could be paid out of deferred debt compensation of senior managers, which would play the role of a performance bond, Dudley said.

“This would increase the financial incentive of those individuals who are best placed to identify bad activities at an early stage, or prevent them from occurring in the first place,” he said, noting that since 2008, fines on big U.S. banks have exceeded $100 billion..

Dudley’s remarks followed a speech by Fed Governor Daniel Tarullo delivered at the same conference in which he said banks may face stiffer rules unless they improve their bad behavior.

“If banks do not take more effective steps to control the behavior of those who work for them, there will be both increased pressure and propensity on the part of regulators and law enforcers to impose more requirements, constraints and punishments,” Tarullo said.