The pressure on municipal bond mutual funds is fading rapidly as a much less panicked tone in the state and local government debt market has stemmed the exodus of cash from the industry.

Municipal funds that report their figures weekly posted a net outflow of $610 million during the week ended Feb. 23, according to Lipper FMI.

This marks a further slowdown from the previous week's $973.9 million outflow, and the fifth straight week of evidence that conditions have eased since the historic $4 billion hemorrhage during the week ended Jan. 19.

Last week's was the lightest outflow since Dec. 8, and the four-week moving average of fund outflows is the lowest since mid-December.

"I'm still experiencing outflows, but they're not as dramatic as they were," said Dick Berry, who manages two tax-free funds with $1.9 billion in assets for Invesco. "People have adjusted to the headline risk they've been reading about. It got overdone for a while and created a selling panic and that's played out by now."

Fund outflows and the performance of municipal debt in the bond market became entangled the past few months in a way that can make it difficult to determine what leads what.

A drastic municipal sell-off that began in November coincided with the beginnings of a record outflux of cash from municipal funds.

Muni bonds delivered a return of negative 5.7% from Nov. 10 to Jan. 19, during which time municipal funds reported redemptions of $29 billion.

Mutual funds and the bond market fell into a negative feedback loop: funds sold bonds to raise cash for investors, forcing more market losses and scaring investors, who redeemed more mutual fund shares.

The municipal bond market began to recover in mid-January, just as outflows were peaking.

In a note to clients, JPMorgan analyst Chris Holmes said the greater stability in the bond market has comforted investors, leading to a slower pace of outflows.

"The snowball momentum of outflows has subsided as investors are likely encouraged by the fact that muni valuations have increased over the last month across all muni sectors," Holmes said.

Municipal bond funds have returned 1.25% so far in February, according to a Lipper index.

As for what brought about the stability in the bond market, many investors and traders report that crossover buyers such as hedge funds and life insurance companies began to find municipal yields — which at the beginning of the month were significantly higher than Treasury yields for anything more than 10-year maturities — appealing.

Purists can also point to the wave of populist uprisings in northern Africa and the Middle East, which have enhanced the allure of safe havens like high-quality dollar-denominated fixed income.

The 10-year Treasury yield has shaved 18 basis points the past 10 days.

This helped to a halt a trend that was likely responsible for at least some of the outflows from municipal funds: the migration from bonds to stocks.

The S&P 500 is up 11.5% since the end of November, and equity funds have reported $30.6 billion in inflows the past six weeks, according to the Investment Company Institute.

The unrest in Libya, among other nations, has somewhat reversed the risk-on trade, with the S&P 500 down 2% last week and investors pulling more than $3 billion from equity funds in the week ended Feb. 23, Lipper said.