A measure of home-price growth raced up in March to an eight-month high, as a limited number of properties for sale ramped up competition among buyers, according to a report released Tuesday.

Home prices rose 2% in March, pushing year-over-year growth to 5.9%, the fastest annual pace since July, said CoreLogic, an Irvine, Calif.–based analysis firm. Seven states, including Texas and New York, have reached new records, and 27 states are at or within 10% of peak price levels.

In February, prices in six states were at record levels.

“All signs are pointing toward continued price appreciation throughout 2015. In fact, the strong month-over-month gain in March may be a harbinger of accelerating price appreciation as we enter the spring selling season,” said Anand Nallathambi, CoreLogic’s chief executive.

There were hints last year that home-price growth could rebound in 2015 as demand rose and supply remained constrained in cities across the U.S. Some economists have raised their forecasts for annual home-price growth, and now see it above 5% in 2016, rather than settling down closer to growth for worker paychecks.

Reports like these worry some observers about an overheating housing market, although nationally, home prices remain 11% below the bubble peak. Markets where prices took the biggest roller coaster ride during the bubble are still hobbled. Home prices are down almost 35% from the peak in Nevada and down 32% from the peak in Florida.

There are pros and cons to rising home prices. Here’s an important pro: Rising prices help struggling homeowners gain equity (one estimate says about 4 million homes are worth less than what’s still owed for a mortgage), sell their home and firm up their personal finances. The major con is obvious: Too-high prices mean that families, especially younger households, can’t afford to buy a home. Home prices are rising faster than wages, making ownership too expensive.

A low supply of homes on the sales market can be a turnoff to potential buyers who want to choose from a variety of properties, but can also lead to bidding wars among investors willing to take the plunge. That’s one of the reasons why the market is seeing rapid housing inflation even as the homeownership rate is at a quarter-century low.

Builders are constructing too few new homes to ease supply pressures, some economists say. But the companies, which have their own struggles with land and labor costs, are wary of building homes that may not be purchased.