The New York City Housing Authority will finally clean house -- at least when it comes to mold.

Lawyers for the city and for NYCHA residents reached a settlement this week stipulating that reports of mold in the city's public housing units will be cleaned up within days rather than months.

That's good news for tenants who have been plagued -- for what seems an eternity -- with the awful allergies and unpleasant odors caused by mold.

But it's especially welcome news for children in public housing. Mold exacerbates asthma, and the city estimates that 25 percent of kids in public housing suffer from that disorder -- far more than the rate for children citywide.

Not only does the settlement acknowledge that mold poses a special health threat to people with asthma, it tells maintenance workers they can no longer tackle the nasty fungus simply by painting over its most visible parts.

From now on they must find and fix the root cause of the problem -- whether it's a water leak, faulty ventilation or uninsulated pipes. They must complete simple repairs within seven days and trickier jobs within 15 days. And they must check back with residents after 60 days to make sure the mold and moisture haven't returned.

A federal judge will monitor the process.

Judicial oversight is often a terrible way to run a public agency. But in this case maybe not. This isn't so much a takeover of NYCHA's famously inept management as it is an enforceable way to fix a specific problem. It will make sure the authority's apartments are kept free of mold so the 400,000 residents who live in them can breathe free.

Beyond mold removal, it will fall to Bill de Blasio to fix NYCHA's other problems after he's sworn in as mayor on Jan. 1. As de Blasio pointed out during the campaign, the city has laws against landlords who fail to provide heat or fix broken elevators. But every day, NYCHA residents see those same conditions and wait years for help to arrive.

One of his first tasks will be to fix the bureaucracy and clear out all NYCHA repair backlogs.

We hope the housecleaning has just begun.