News flash for anyone looking for a house on the cheap: Foreclosed homes probably aren’t the bargain you’re expecting, and certainly not the bargain they were several years ago.

Nationally, the average discount on a foreclosure in September was only about 8 percent below market value, according to an analysis by Zillow. That’s a significant change from the 24 percent average markdown in 2009, during the depths of the housing bust, and another signal that the country’s housing market is inching toward recovery.

“There’s no such thing as a fire sale on a foreclosure right now,” said Marc Joseph, a real estate agent in Fort Myers, Fla., who has carved a profitable niche in recent years selling foreclosures in the Sunshine State. “We’re getting back to that point where if something good hits the markets, we’re getting multiple offers again. That’s been happening the past six months.”

That doesn’t mean there aren’t deals to be found in certain markets. According to Zillow, the highest discounts can be found on foreclosures in the Pittsburgh area, at 27 percent. Cleveland, Cincinnati and Baltimore have average markdowns on foreclosures topping 20 percent.

But in many hard-hit markets, particularly ones where home prices fell sharply and investors and buyers have swooped in to buy up foreclosures, discounts have all but vanished. Zillow found that in Las Vegas and Phoenix, there is “no discernible difference” between foreclosure and non-foreclosure sales. Discounts have shrunk to less than 1 percent in Sacramento, 3 percent in the Miami-Fort Lauderdale area and barely 4 percent in Los Angeles.

The average foreclosure discount in the Washington area is 5.5 percent, according to the analysis.

Stan Humphries, Zillow’s chief economist, wrote recently that foreclosures often can seem like a bigger bargain than they are when comparing sale prices of foreclosed homes with those of non-foreclosed homes.

“The typical foreclosure property is likely quite different than the typical non-foreclosure property,” Humphries wrote, noting that less expensive homes are more likely to be in foreclosure than pricier homes, giving buyers “unrealistic expectations about the discounts they will find when shopping for foreclosures.”

In many parts of the country, the shrinking discounts on foreclosures have resulted in part from a shrinking number of foreclosed homes for sale. As the economy has improved, fewer homeowners have defaulted on their mortgages. In addition, banks increasingly have begun to favor short sales, loan modifications and other alternatives that keep people in their homes, avoiding the expensive and time-consuming process of foreclosure.

Some analysts and agents have speculated that banks are holding a massive “shadow inventory” — homes that have gone through foreclosure but have yet to be put up for sale — that eventually could flood certain markets and push prices down again. That scenario has yet to materialize.

Instead, foreclosure inventories have remained low in many places, creating fierce competition and driving up prices.

“There are buyers, but unfortunately there are not a lot of foreclosures. . . . I started getting multiple offers about a year ago on my [foreclosure listings],” said Shirley Noel-Williams, a Re/Max agent who specializes in foreclosures in the District and numerous counties in Maryland, including hard-hit Prince George’s. “Buyers are having a very difficult time. The market is mostly short sales right now, and they don’t close very quickly.”

Noel-Williams said she currently has only two foreclosure listings, and those she has gotten during the past year have drawn multiple offers. She has begun taking on more short sales and more traditional home sales to make up for the lack of foreclosures.

“As the market changes, I have to change,” she said.

Joseph, the Florida real estate agent, said he recognizes that the falling number of foreclosures is a good sign for the health of the housing market, but he also has witnessed the frustration among buyers who expect bigger discounts.

“They’re very surprised,” he said. “They’re coming down, and they’re figuring out that last year’s prices are gone. They’re not getting the deals they were two or three years ago.”