On Tuesday, the Fed chair faced grilling from the new Republican Senate. She came prepared first and foremost to dissuade lawmakers from supporting so-called “Audit the Fed” legislation proposed by Kentucky Senator and likely presidential hopeful Rand Paul and cosponsored by 30 other legislators. The bill would, among other things, increase Congress’ ability to oversee the Fed’s interest rate decisions.

“I strongly oppose Audit the Fed,” said Yellen during questioning, arguing that it would “bring short-term political pressures to bear” on the central bank and dissuade it from making the “hard choices” needed to keep inflation in check. She said that in cases where countries have suffered from excessive inflation, the central banks managing those economies often kept monetary policy too loose due to political pressure to boost economic growth.

But if you watched Tuesday’s hearing closely, there didn’t seem to be much appetite for getting Congress involved in interest rate decisions so much as a general dissatisfaction with the distribution of power at the central bank. Republican Senator Bob Corker tossed Yellen a series of softballs on the audit question, allowing the chair to explain the degree to which its assets are already audited by independent firm Deloitte and the fact that the Fed’s balance sheet is published online.

But senators on the right and left lobbed several criticisms at the Federal Reserve. Senate Banking Committee Chair Richard Shelby began his questioning by asking for Yellen’s opinion on a recent proposal by outgoing Dallas Fed President Richard Fisher that the Fed be reorganized to make the Federal Reserve Bank of New York much less powerful and distribute that influence to other regional banks. Fisher argued that making the President of the New York Fed at all times the Vice Chairman of the Federal Reserve Board of Governors gives too much power to a regional bank that has very close ties to Wall Street’s biggest and most powerful banks.

Democratic Senator Jack Reed of Rhode Island, who recently submitted legislation that would require the President of the New York Fed to be confirmed by the Senate, echoed Shelby’s concerns. He called attention to recent media reports that suggested that regulators at the New York Fed have been successfully cowed by the very institutions they are supposed to be regulating. The Federal Reserve is reviewing whether the New York branch is in fact too close to Wall Street, but the results of that study have yet to be made public.

According to Chris Krueger, an analyst with Guggenheim Securities, Congress is more likely to take some power away from the New York Fed than it is likely to expose interest rate decisions to further oversight. In a note to clients, he writes:

It is our belief that some version of the Fisher Plan becomes the new Audit the Fed bill and it is something that the Federal Reserve Board will have much more trouble stopping because it will feed upon anti-New York/anti-mega bank bias that exists in Congress. While the Federal Reserve Board may have objections to the Fisher Plan, it is certainly more palatable than the current Rand Paul bill – and also far less likely to spook markets.