It is not very often that business people head to Washington to explain how unimportant they are.

But over the last several months, executives from more than two dozen financial companies and their trade groups have paraded into the Treasury Department, the Federal Reserve and other government agencies to try to persuade top regulators that they are not large or risky enough to threaten the financial system if they should ever collapse.

Big insurers like the Mass Mutual Financial Group and Zurich Financial Services; hedge funds like Citadel and Paulson & Company; and mutual-fund companies like BlackRock, Fidelity Investments and Pacific Investment Management Company have all been making the rounds, according to documents filed by the regulatory agencies.

What they are all hoping to avoid is being designated “systemically important” by a council of financial regulators. That would require them to face stricter federal oversight and keep more cash on hand, which they fear would erode profits.

Jeffrey A. Goldstein, the Treasury undersecretary for domestic finance, finds the arguments so familiar that he has opened some meetings by asking the firms if they would like to designate themselves as systemically important. “I can’t recall a firm that came in and said yes,” he said.