Even some of the cities that suffered the most in the housing bust are showing signs of improvement, with prices beginning to recover in places like Miami, Atlanta and Detroit, according to the latest housing data.

In fact, there is improvement across the board, with home prices nationally inching up over their levels a year ago for the first time since 2010, when sales were helped by a temporary tax credit for home buyers.

The data is contained in the S.&P./Case-Shiller Home Price Index, which tracks prices nationally and in 20 major cities. Both showed gains over the past year, from June to June — 1.2 percent nationally, and 0.5 percent in the 20 cities. Though prices were still depressed in a few of the cities compared with a year ago, every one of them showed price gains from May to June. The report is highly regarded because it tracks actual price differences as a home is sold and resold over time. See the rest of the story www.nytimes.com.