Fewer people applied for unemployment benefits last week, a sign that the job market may be improving slightly. While that boded well for the economy, a separate report showed worker productivity fell this spring at a faster pace than previously estimated while labor costs were rising at a faster clip. Both developments could pose threats to a fragile economic recovery. The Labor Department says weekly applications fell 12,000 to a seasonally adjusted 409,000 last week, the first decline in three weeks. A strike by Verizon workers drove applications higher during the previous two weeks. The strike ended last week and is no longer affecting applications. Applications have fallen from an eight-month high of 478,000 in April. Still, they typically need to drop below 375,000 to signal sustainable job growth. They haven't been at that level since February. The drop suggests employers aren't stepping up layoffs amid renewed concerns about the economy's health. Still, a sharp reduction in growth has fueled fears that the economy could be on the verge of another recession. Productivity declined at an annual rate of 0.7 percent in the April-June period, a bigger drop than the 0.3 percent decline reported a month ago. Labor costs rose at an annual rate of 3.3 percent, faster than the 2.4 percent increase originally reported. The changes reflected downward revisions made last week to overall economic growth which showed the economy's output barely growing in the spring. Declining productivity, if it persists for a prolonged period, would represent a serious economic threat while rising labor costs would cut into corporate profits.