LET'S KEEP BUYING THOSE FORECLOSURES

After a plunge lasting three years, houses have finally become cheap enough to lure buyers. That, in turn, is stabilizing prices, generating hope that the real estate market is beginning to recover.

Eight cities, including Chicago, Cleveland, Denver and San Francisco, showed price increases in May, up from four in April and one in March, according to data released Tuesday. Two other cities, Charlotte, N.C., and New York, were flat.

For the first time since early 2007, a composite index of 20 major cities was virtually flat, instead of down.

"We've found the bottom," said Mark Fleming, chief economist for First American CoreLogic, a data firm.

The release of the surprisingly strong Case-Shiller Price Index, compiled by Standard & Poor's, followed earlier reports that sales of existing homes rose last month for the third consecutive time, while sales of new homes rose in June by the largest percentage in eight years

All of these improvements are tentative, and come after a relentless decline that knocked more than half the value off houses in the worst-hit cities.

Some skeptics say they believe the market is merely pausing before it resumes falling and that much of the life in the market is coming from speculators. Even the most enthusiastic analysts acknowledge that rising unemployment, another leap in foreclosures or a significant jump in interest rates could snuff out progress.

Still, hope is growing in some quarters that the worst has passed.