Call it a sliver of a silver lining for America's beaten-down housing market: The inventory of troubled U.S. homes not yet listed for sale is diminishing.

Homes in foreclosure -- or headed into foreclosure -- are being sold at a fast enough clip to chip away at the so called "shadow inventory" that hangs over the U.S. market, Santa Ana data provider CoreLogic reported Tuesday. Shadow inventory at the end of July was down to 1.6 million units, representing a five-month supply of homes. 

That means that there are 1.6 million homes in the pipeline not listed for sale. This is down from 1.9 million units, a six-month supply, from about a year ago.

"The steady improvement in the shadow inventory is a positive development for the housing market," CoreLogic Chief Economist Mark Gleming said. "However, continued price declines, high levels of negative equity and a sluggish labor market will keep the shadow supply elevated for an extended period of time."

The company derives the estimate for shadow supply, or pending supply, by taking the number of so-called distressed properties not listed on any real estate listing services. It considers distressed properties to be those that are either bank-owned or delinquent by three-plus months.