Washington ? Single-family home construction posted a modest rebound in April, raising hopes that the three-year slide in housing is leveling off. But a bulging supply of unsold homes, record levels of foreclosures and still-falling home prices suggest a sustained recovery isn’t likely until next spring at the earliest.

The Commerce Department said construction of homes and apartments fell 12.8 percent last month to a seasonally adjusted annual rate of 458,000 units, the lowest pace on records going back a half-century.