In September, the number of positions waiting to be filled in the U.S. rose to the highest level in more than three years. This may indicate that some companies are preparing for an improving economy.

The Labor Department data showed today in Washington, that job openings increased by 225,000 to 3.35 million, the most its been since August of 2008, a month before the collapse of Lehman Brothers Holdings Inc. intensified the financial crisis. As the firings climbed, hiring advanced by 185,000 to 4.25 million.

The Labor Department figures showed last week that payrolls grew by 80,000 workers in October, and gains in the prior two months were revised up. At the same time that all this is happening, hiring is short of the pace needed to lower unemployment hovering around 9 percent, thus helping to explain why Federal Reserve Chairman Ben S. Bernanke has said that the recovery is ”frustratingly slow.”

”It is reassuring that the economy could muster a speed-up in job openings,” said Henry Mo, who is a senior economist at Credit Suisse in New York. And at the same exact time, ”we have a persistent but inadequate recovery. We need faster hiring.”

In September, openings increased 7.2 percent from a revised 3.13 million in the prior month that was higher than previously guessed.

According to today’s report, the rate of job openings rose to 2.5 percent. The employers in the professional and business services and trade and transportation accounted for the biggest increases in available employment. Construction was the one and only industry to show a substantial drop.

The report helped to shed some light on the dynamics behind the monthly employment figures. The Labor Department figures showed on November 4, that payrolls climbed last month following gains in the prior two months that were revised up by 102,000. Private payrolls rose substantially rose by 104,000 workers last month, less than the median projection in a Bloomberg survey.

Credit Suisses’s Mo said that given today’s numbers, an upward revision to October payrolls ”could be possible.”

Today’s figures indicate that there are more than 4 people vying for every opening, compared with the 14 million Americans who were unemployed in September, the numbers are up from about 1.8 when the recession began in December 2007.

Today’s report showed that the employers took on 4.25 million workers in the month of September, the numbers were up from 4.06 million the previous month.

The total amount of firings, which also excluded retirements and those who left their jobs voluntarily, climbed up to 1.76 million from the previous 1.69 million a month before.

Today’s report showed that the economy created a net 1.3 million jobs in the 12 months ended in September, representing 48.3 million hires and about 47 million separations.