BIG CHANGES ARE UNDER WAY AT THE NATION'S 3,100 public housing agencies. A new rule is changing both the criteria by which they receive money and how they operate.

Under a 30-year-old formula, housing agencies received an operating subsidy ($3.6 billion nationwide) meant to make up for any of their costs not covered by resident rents. Housing officials long criticized the formula for its tenuous link to reality, and HUD contracted with Harvard University to develop an improved cost model.

When the dust settled, a disparity emerged: Housing agencies in the North and Midwest stand to lose funding under the new formula, while many agencies in the South will gain. That's largely because the original formula failed to predict well for small agencies, which dominate the South, says Christine Siksa, of the National Association of Housing and Redevelopment Officials. To smooth the transition, funding decreases will be phased in over five years; increases will take two.

But HUD offered agencies a carrot: If they can become compliant with new management guidelines by Oct. 1, 2005, their losses will be capped at 5 percent.