Municipal bond mutual fund outflows moderated last week as a nervous market seemed better able to absorb the relentless fund selling.

Investors redeemed $1.9 billion from municipal funds during the week ended Jan. 26, according to Lipper FMI.

Until three months ago, this would have been considered a severe outflow. Last week, it was good news.

Municipal funds have reported $31.19 billion of outflows the last 11 weeks, easily the heaviest exodus of cash in that amount of time ever.

The four-week moving average of outflows is a record $3.64 billion. The latest outflow is half the previous week’s.

“There’s still pretty ­pervasive fear in the muni market,” said Chris Johns, who manages a $272.9 million Colorado fund for Aquila Group of Funds. “The fear for the individual investor that’s taking money out of municipal bond funds is still there. It’s starting to subside a little bit, but it’s still a very fragile situation.”

The withdrawal of cash from the $471.8 billion municipal fund industry triggered an avalanche of selling beginning in November as mutual fund managers were forced to sell bonds to raise cash to meet redemptions.

A Bloomberg LP index tracking bids wanted on municipal bonds spiked to a record $1.4 billion in December and remained far above the long-term trend for most of the fourth quarter and January. Market participants said the bids were being sought mostly by mutual fund complexes scrambling to raise cash.

This dynamic is largely responsible for a nearly 100 basis point demolition of 30-year triple-A tax-exempt bonds since the end of October. Municipals returned a negative 7% from the end of the third quarter through the first two weeks of January, according to a Standard & Poor’s index tracking the sector.

The market began to rally in the second half of January. The 30-year yield has tumbled more than 25 basis points the past two weeks. While mutual fund outflows drove much of the selling, they clearly aren’t driving the buying.

The peak in yields came during a week when investors withdrew $4 billion from their funds, the most in history by far.

Johns believes municipal bond dealers, sensing bargains, began stepping up and buying bonds for their own inventories.

Municipal Market Data surveys traders each week about their outlook for yields. For all of the fourth quarter, a very small percentage of dealers was bullish, with the bulls polling at 0% for several weeks.

Last week, 38% described themselves as bulls, the strongest reading since August.

“You’ve seen dealer inventories rise a little bit,” Johns said. “What’s happened is some of the bigger dealers were starting to position bonds at prices they thought were attractive as trading vehicles. That’s what I point to as really helping. … They were a little bit more willing to use some of their capital to take on inventory when they thought they could sell it to the retail investor.”

Evan Rourke, a portfolio manager at Eaton Vance, thinks crossover buyers like insurance companies also stepped in to take advantage of “excellent relative value.”

The 10-year triple-A muni bond yield reached as high as 104% of the 10-year Treasury earlier this month. The average since 1980 is about 80%, according to MMD.

The 30-year muni-Treasury ratio neared 110% earlier this month.

Rourke is hopeful the worst of the mutual fund bleeding is over. He pointed out that municipal funds grew rapidly after the financial crisis as a lot of “hot money” chasing yield flooded the industry. Much of this was never meant to be a long-term commitment to the sector, Rourke said.

Investors stuffed municipal funds with more than $100 billion in cash in 2009 and the first 10 months of 2010, according to the Investment Company Institute. They have withdrawn more than $30 billion since the end of October.

Rourke believes that $30 billion represents most of the inflows that were intended to be temporary.

“I think we’ve washed out the fast money,” he said. “My thinking is that the investors who are in the market now are probably a little more committed to being in munis.”

Market gains prevented municipal funds from bleeding assets despite the outflows last week as municipals returned 1.1% for the week. Muni funds reported $3.05 billion in market gains, more than offsetting the outflows.