The United States lost jobs in July, but the pace of firings and layoffs is moderating, according to a private employment report.

Overall, the US private nonfarm sector lost 371,000 jobs last month, according to the ADP National Employment Report (.pdf) released Wednesday. That estimate, intended to anticipate the official government estimate to be released Friday, was slightly higher than many economists had forecast. Nevertheless, it represents the smallest number of job losses reported by ADP since October 2008 – and roughly half the peak job loss of 736,000 in March.

“Despite recent indications that overall economic activity is stabilizing, employment, which usually trails overall economic activity, is likely to decline for at least several more months, albeit at a diminishing rate,” Joel Prakken, chairman of Macroeconomic Advisers, said in a release. The company puts out the monthly report, based on payroll data, in partnership with Automatic Data Processing.

Job losses have slowed the most at small- and medium-sized businesses, where the monthly rate of decline now is half what it was in January, according to the ADP report. Large companies (those with 500 or more employees) have seen their job losses slow by slightly more than a third in the same period.