Home prices are still falling, but the rate of decline - at least locally - has slowed, according to the Standard & Poor’s Case-Shiller Home Price Index.

Boston was one of only three major U.S. cities where home prices fell in the single digits while the rest of the nation saw double-digit losses. Case-Shiller tracks sales in 20 cities. In Boston, prices were down 7.7 percent in April compared to a year ago. Prices in Sun Belt cities like Las Vegas and Phoenix fell by a third.