New U.S. claims for unemployment benefits fell last week to their lowest since early April and the trade deficit unexpectedly shrank in September, pointing to a slight improvement in the economy.

The Labor Department said initial claims for state unemployment benefits fell for the second straight week, down 10,000 to a seasonally adjusted 390,000.

The U.S. labor market is still a long way from recovering from the deep 2007-2009 recession, but analysts said the data at least reinforced the view that the healing process was continuing.

Clearly, the labor market is improving, but at a very slow pace, said Omer Esiner, chief market strategist at Commonwealth Foreign Exchange in Washington.

In a separate report, the Commerce Department said the seasonally adjusted U.S. trade deficit shrank to $43.1 billion in September.

That was its narrowest since December thanks to record-high exports and suggests the U.S. economy closed the third quarter a little stronger than many expected.

Also, imports from China fell 2.5 percent from a month earlier, although that reading was based on non-seasonally adjusted figures.

Prices for U.S. government debt extended losses on the claims and trade data.

Investors remain focused on the unfurling debt crisis in Europe, which economists say could easily send the United States back into recession.

Weekly jobless claims still remain well above pre-recession levels and have dipped below 400,000 -- a threshold many economists believe signifies improving labor market conditions -- only 10 times over the past year.

A Labor Department official said a freak fall snowstorm that kept many people housebound in the Northeast did not affect initial jobless claims.

(Reporting by Jason Lange and Lisa Lambert, Editing by Chizu Nomiyama)