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.

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Home Prices in Selected Cities, Through May 2009

 Today's Business: David Streitfeld on Signals From the Housing Market

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Marc Serota for The New York Times

Kirit Shah, his wife, Jayshri, and son, Parth, are decorating their house in Royal Palm Beach, Fla.

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.

“Recession is over, economy is recovering — let’s look forward and stop the backward-looking focus,” John E. Silvia, the Wells Fargo chief economist, wrote Tuesday in a research note.

Kirit Shah decided to look forward a few weeks ago. A retired forensic chemist for the New York Police Department, he closed on a house in Royal Palm Beach, Fla.

Mr. Shah was not dissuaded when the salesman at K. Hovnanian Homes told him the five-bedroom place had been empty since it was finished three years ago. “It was waiting for me,” said Mr. Shah, 64. “I’m on a lakefront. I never dreamed I would be on a lakefront. I’m within walking distance of a swimming pool.”

But the thing he likes best is this: he paid $260,000 for the five-bedroom house, half of what that model was fetching during the boom. “An excellent deal,” he said. “Plus I got a good rate on my mortgage, under 5 percent.”

Turning markets are full of uncertainty. If Mr. Shah was one reason new home sales were up 11 percent in June from May, it is unclear just how many others like him are out there.

Brad Hunter, chief economist for Metrostudy, a research firm, said the new home numbers appeared to illustrate less a return of buyers like Mr. Shah and more a resurgence of investors and speculators. Metrostudy’s own data showed that the number of buyers during the second quarter who actually moved into their new house declined 2.6 percent.

“Investors are turning right around and putting the houses on the market for sale or for rent,” Mr. Hunter said. “What appears to have been an absorption of excess inventory can be just a changing of ownership of that inventory.”

The good news in the Case-Shiller index, the most widely watched source of price information about the housing market, is equally provisionary. Tracking only large urban areas, the monthly index does not represent the country as a whole.

The Case-Shiller figures released Tuesday showed May prices were down 17.1 compared with May 2008. As bad as that may sound, it was the fourth consecutive month that price declines slowed — a step in the right direction, but perhaps not cause for widespread celebration.

More attention was focused on the news that, when May was compared with April, the price index for 20 major cities showed a half-percent gain. It was the first month-over-month increase in the index in 34 months.

“It is very possible that years from now we will say that April 2009 was the trough in home prices,” said Maureen Maitland, vice president for index services at Standard & Poor’s.

When the numbers were adjusted for seasonal factors, however — the usual way housing figures are presented — the slight gain disappeared and the index was essentially flat. Half of the cities showed continued declines.

One reason the market is perking up in some places, real estate agents say, is the encouragement offered by such measures as the first time buyer’s tax credit of $8,000.

All the more reason, said the National Association of Realtors, to not only extend the credit but expand it. The association is lobbying for the current credit, which expires in December, to be replaced with a $15,000 credit for all buyers.

“This is a relatively low-cost way to keep the housing market moving forward,” said Paul Bishop, the association’s managing director of research.

Another reason for the market’s resurgence is the prevalence of foreclosures, which make up about a third of all existing home sales. In some troubled regions, agents say they cannot remember the last transaction that did not involve a bank disposing of a property.

These communities are not yet showing any improvement in prices. Las Vegas was the worst-performing city in the May Case-Shiller index, falling 2.6 percent. Prices have fallen there by a third in the last year.

“The mom and pop that work at the Hilton can now afford a home here again,” said Justin Pechonis, a Las Vegas real estate agent. “Las Vegas is a great place to buy now.” But not from him. Sickened by seeing so many clients foreclosed on, he is getting out of the business. He now drives a taxi.

All this uncertainty breeds a hesitancy that seems to show up in nearly every sale, especially at the higher end of the market. When Margot and Pascal Lalonde decided in April to sell their two-bedroom condominium in the North End of Boston, they methodically quizzed six experienced agents about a good price.

List it for under $500,000 unless you want to be here for months, said one agent. Two others said they should demand $675,000. The other three were in between.

“In a market with so few sales, no one knows what to do,” said Ms. Lalonde, a consultant.

After 80 days on the market and two small price reductions, the condo is now under contract for $550,000. The buyers examined the apartment six times. The Lalondes, who are moving to Short Hills, N.J., expect to be no less careful when they buy.