Americans think their money is safe in their banks–but they’re more split regarding exactly how secure those institutions are. At least nine in 10 respondents said that they feel their money is safe at their bank or credit union, regardless of its size, according to a new Harris Poll survey of 2,054 Americans, whose responses have been weighted for age, sex, race and ethnicity, education, region, household income, and propensity to be online to bring them into line with their actual proportions within the U.S. population.

This is good news for banks, assuming that Americans act on their beliefs or, more precisely, don’t act by pulling their money out, which would exacerbate the banking crisis. Surprisingly, the customers of small financial institutions were slightly more likely to believe that their money is safe (93%) than the customers of medium and large banks. The remarkable disconnect between how safe the public believes their money is and the state of the institutions in which it resides is likely due to the federal government’s proclaimed backstop for depositors at Silicon Valley Bank and Signature Bank, as well as the rescue of First Republic by large banks.

Federal law protects deposits of up to $250,000 in FDIC-insured institutions but the Silicon Valley and Signature bailout–where more than 90% of deposits were uninsured because they exceeded that threshold–took care of every depositor, regardless of account size. That has raised the question of whether the Fed will now bail out accounts of any size.

While Federal Reserve Chairman Jerome Powell recently told reporters that the Silicon Valley and Signature bailouts “demonstrate that all depositors' savings in the banking system are safe,” Treasury Secretary Janet Yellen has ruled out universal deposit insurance as “not something we have looked at…not something we're considering."

Judging by our survey, Americans expect something like the Powell declaration will play out. However, judging by the S&P 500’s net 1.7% drop after Yellen backtracked, markets still have Yellen-powered jitters.