WASHINGTON - The number of Americans applying for unemployment benefits fell last week to its lowest level in nearly 21/2 years, a sign that the job market is slowly improving.

Applications dropped by 34,000 to 388,000, the fewest since July 2008, the Labor Department said Thursday. The number of applications has either fallen or remained unchanged in five of the last six weeks.

The rule of thumb for economists is that fewer than 425,000 new people seeking unemployment benefits signals modest job growth. But they also caution that applications need to fall consistently to 375,000 or below to bring down the unemployment rate. Applications for unemployment benefits peaked during the recession at 651,000 in March 2009.

The latest report, which covers the week that ended on Christmas Day, is considered by some economists to be less reliable than most. One reason is that many state offices close for at least one day. Other seasonal factors make the report more volatile.

Still, a department analyst said that there were no unusual factors affecting the report and that it considers the effect of the holiday.

Economists said that what matters most is the downward trend.

"If we can continue this improving trend, we'll likely see stronger job growth in 2011," said Benjamin Reitzes, an economist at BMO Capital Markets.

A separate report showed that the number of people who signed contracts to buy homes rose in November, the fourth increase since contract signings hit a low point in June.

The National Association of Realtors said its index of sales agreements for previously occupied homes increased 3.5 percent last month from October. Still, this year's pace of completed home sales - which the Realtors group measures in a separate report - is shaping up to be the slowest in 13 years.