Inflows to municipal bond mutual funds, while still robust, have fallen for a second straight week.

Muni bond funds that report their flows weekly saw $871 million in inflows for the week of Jan. 23, Lipper FMI numbers showed. That compared with inflows of $1.44 billion the week ended Jan. 16, and $1.55 billion the week before that.

Muni yields mostly hovered on the week, giving up a mere basis point or two despite a hefty uptick in volume arriving midweek. They held pace with Treasury yields beyond the front end of the curve.

New issuance picked up again and was reasonably well received. Traders noted some effort to unload some volume into the secondary.

Since negative flows closed out 2012, January has mostly been in the black. The market has seen three straight weeks of inflows from weekly reporting muni bond funds. Prior to that span, the market had seen three consecutive weeks of outflows, marked by a peak of $2.3 billion exiting the market for the week of Dec. 19.

Assets for all muni funds that report their flows weekly increased for a fourth consecutive week to $325.6 billion, from $324.8 billion the week before.

The value of the holdings for weekly reporting funds was positive for a fifth straight week, rising by $293 million. The week before, it increased by $1.28 billion.

The four-week moving average for all municipal bond mutual funds that report their flows weekly was $965 million of inflows, up from $641 million the week before.

It was a strong week for long-term bond funds that report their flows weekly. They reported heavy inflows for a third consecutive week, at $579 million, representing a decrease from the $917 million of inflows they reported the week before.

High-yield muni funds also reported inflows for a third straight week. They were positive for most of 2012.

High-yield funds that report weekly saw $279 million in inflows, Lipper said. The previous week, they reported $434 million in inflows.

Assets for high-yield funds that report their flows weekly rose for a fourth straight week to $44.76 billion, up from $44.73 billion the week before.

The value of the holdings for weekly reporting high-yield funds rose by $97 million. Last week, they rose by $285 million.

The four-week moving average for all high-yield municipal bond funds that report their flows weekly was $222 million of inflows, rising from $87 million of inflows the week before.