SEATTLE—The National Association of Realtors may be reporting that growth in home prices—including for-sale apartments along with single-family houses—moderated last month, but Zillow is taking a long-term view. Within the next year, Seattle-based Zillow predicts, home values in more than 1,000 US communities will be higher than ever.

Although home values nationwide are still 13.5% below their 2007 peak, Zillow says the housing recession is “almost entirely in the rearview mirror” in 1,080 of the more than 8,700 cities and towns it covers. They’re expected to surpass their pre-recession peaks by the first quarter of 2015, if they haven’t done so already.

“This is a remarkable milestone coming only two and a half years after the end of the worst housing recession since the Great Depression, and is a testament to just how robust this housing recovery has been,” says Stan Humphries, Zillow’s chief economist. “So far, this steady appreciation has not created affordability issues in the majority of places. But there are a handful of markets where affordability is again a challenge, even with mortgage interest rates incredibly low.”

Those markets include the major California cities: in San Francisco, Los Angeles, San Jose and San Diego, the share of residents’ incomes currently devoted to monthly mortgage payments exceeds historic norms, Zillow says. Not surprisingly, the West also saw the highest year-over-year appreciation in median home prices, according to the Washington, DC-based NAR: 12.6%, compared to 3.2% in the Northeast, 5.9% in the Midwest and 6.7% in the South. The region also saw the steepest Y-O-Y decline in home sales: 13.4%, NAR says.

Among the more than 300 metro areas covered by Zillow, home values in 60 have already exceeded their pre-recession peaks or are expected to do so in the next year. They include Dallas, Houston, Denver, Pittsburgh, San Antonio, San Jose and Austin.

NAR on Tuesday reported that sales of existing homes crept downward by 0.2% to a seasonally adjusted annual rate of 4.59 million in March from 4.60 million in February. The figure is also 7.5% below the 4.96-million-unit pace the year prior. Last month’s sales volume remained the slowest since July 2012, when it was also 4.59 million.

“There really should be stronger levels of home sales given our population growth,” says Lawrence Yun, chief economist at NAR. “In contrast, price growth is rising faster than historical norms because of inventory shortages.”

Sales of single-family homes in March were unchanged from the prior month at a seasonally adjusted annual rate of 4.04 million, while the median existing single-family home price was $198,200 in March, up 7.4% from a year ago. In the multifamily arena, existing condominium and co-op sales declined 1.8% to an annual rate of 550,000 units in March from 560,000 in February. The median existing condo price was $200,800 in March, up 11.6% from March ‘13.

In the area of rentals, Zillow says that rents rose 2.7% Y-O-Y in the first quarter and 0.9% compared to the Q4 ’13. US rents have risen year-over-year for more than two years running, according to Zillow.