U.S. home prices are slowing down, with easing annual growth in 20 major cities bringing the market closer to normality, according to data released Tuesday.For a fourth consecutive monthly gain, U.S. home prices rose 1% in June, pushing annual price growth to 8.1%, the leanest year-over-year result since January 2013, according to the S&P/Case-Shiller's 20-city composite index of 20 major cities released Tuesday.For the first time since early 2008, each of the 20 cities saw annual price growth slow down. Slower home-price growth, along with indicators such as a more positive outlook among home builders, are a good sign, said David Blitzer, index committee chairman at S&P Dow Jones Indices."Taken together, these point to a more normal housing sector," he said.Among 20 tracked cities, all saw higher home prices in June, led by a monthly increase of 1.6% New York, the city's strongest showing since June 2013.After seasonal adjustments, home prices among the 20 cities declined 0.2% in June, compared with a drop of 0.3% in May.Prices have been cooling thanks, in part, to more sellers placing their homes on the market. Slower home prices can support more purchases by encouraging buyers to make an offer. Home prices that run too hot for too long would cut out an increasingly large share of the pool of prospective buyers. Buyers also have to contend with rising mortgage rates, which spiked last year, though there's been some easing in recent months."The evidence suggests that house prices are leveling off following the sharp increases of 2013, with the improved supply we have seen in recent existing home sale figures putting a cap on price pressures, and demand still below last year's peaks," Andrew Grantham, an economist at CIBC World Markets, wrote in a research note.While buyers don't love quickly rising home prices, fast appreciation isn't all bad. Millions of troubled properties have regained equity over the past year, though this effect may wane somewhat as price growth slows."A more gradual pace of home price appreciation should continue to lift more homeowners out of negative equity, albeit at a slightly slower pace," Gennadiy Goldberg, U.S. strategist at TD Securities, wrote in a research note.Including June's monthly gain, home prices were about 17% below a 2006 peak.Separately, the Federal Housing Finance Agency, which tracks deals involving mortgages backed by Fannie Mae (FNMA) and Freddie Mac (FMCC), reported that its seasonally adjusted gauge of home prices rose 0.4% in June, the seventh consecutive gain. Compared to June 2013, prices were up 5.1%, the FHFA added.