Construction of new homes edged up slightly in September, helped by a rebound in single-family construction. But applications for building permits fell by the largest amount in five months, a worrisome sign for future housing work.

Construction of new homes in the U.S. rose in June to the highest level in seven months, a sign that builders are starting to regain confidence as they emerge from the housing bust. In Chesterfield County, permits for single-family houses rose to the highest level in 10 months. But the 70 permits issued in June was still down 31 percent from the same month a year ago.