Flows to muni bond mutual funds, though still negative, recovered much of their lost ground over the previous two weeks.

Those funds that report their flows weekly recorded outflows of almost $13 million for the week ended Jan. 2, Lipper FMI numbers show. That’s up from the week ended Dec. 26, which saw outflows of $423 million from weekly reporting funds.

Two weeks ago, funds that report their flows weekly lost $2.31 billion. That stands as the heaviest outflows since early 2011, and further brought 2012 flows to a close with a decidedly negative feel.

In fact, the market saw just four down weeks all year, including the final two weeks of 2012. Before the outflows, muni bond mutual funds had recorded 63 weeks of positive flows in the 67 weeks.

This week, tax-exempt yields largely hovered until the New Year arrived and rates rolled over. In addition, Congress agreed on a temporary solution to the fiscal cliff, lifting yields on Treasuries. Munis followed, albeit at a far slower pace.

Assets for all muni funds that report their flows weekly rose after falling for three consecutive weeks to $318.2 billion, from $317.6 billion the week before.

The value of the holdings for weekly reporting funds was positive for the second consecutive week in a month, rising by $674 million. The week before, it rose by $351 million.

The four-week moving average for all municipal bond mutual funds that report their flows weekly was $610 million of outflows, down from a $484 million loss the week before.

Long-term bond funds that report their flows weekly reported a third straight week of heavy outflows, at $294 million. This represented a small rise from the $353 million of outflows they reported the week before.

High-yield muni funds also saw robust outflows for a third straight week, though the hemorrhaging is shrinking. Flows had been positive for an overwhelming majority of last year before the shift.

High-yield funds that report weekly saw $104 million in outflows, Lipper said. The previous week, they reported $261 million in outflows.

Assets for high-yield funds that report their flows weekly rose after decreasing for two consecutive weeks to $43.28 billion, up from $43.11 billion the week before.

The value of the holdings for weekly reporting high-yield funds increased by $115 million. Last week, they rose by $43.7 million.

The four-week moving average for all high-yield municipal bond funds that report their flows weekly was $284 million of outflows, dropping from $205 million of outflows the week before.