Following a disappointing report from ADP on Wednesday, the labor market got some decent news from Washington on Thursday showing that fewer Americans filed for first-time unemployment benefits in the week ended June 1 than the week prior.

The Labor Department said that initial jobless claims dropped by 11,000 to a seasonally adjusted 346,000 last week from a revised 357,000 (revised upward from 354,000). On average, economists were expecting a drop to 345,000, what would have been a drop in claims of 9,000.

There was no unusual data in this week’s figures and no states were estimated, according to the Labor Department.

The four-week moving average, regarded as a better gauge of labor trends because it eliminates weekly volatility, increased 4,500 to 352,500. It was the second week in a row that the one-month average rose, taking it to six-week highs.

Continuing claims, those people already collecting benefits excluding people claiming benefits from federal programs, decreased by 52,000 to 2.952 million for the week ended May 25. Continuing claims are reported at a one-week lag compared to initial claims. It was the second time in three weeks that the continuing claims figure improved.

Total claims, which count all the people receiving benefits under all state and federal programs, increased to 4.647 million in the week ended May 18 from 4.579 million in the week earlier.

The states posting the biggest jump in first-time applications for benefits were California (+8,622), Missouri (+2,999) and Kentucky (+1,750). Those with the greatest declines were Michigan (-2,185), North Carolina (-1,747) and South Carolina (-867).

Employers have been keeping staff levels relatively consistent despite fears that increased taxes and federal budget cuts as part of the so-called sequester earlier this year would dampen job’s trends. The four-week moving average, however, has now pushed above the 350,000 mark that economists generally claim is indicative of moderate jobs growth.

ADP’s report yesterday showed that the country added 135,000 new jobs in May, far below the 167,000 that economists predicted, sparking resurgence in fears the sequester cuts are taking a toll on the economy and a sell-off on Wall Street.

The two reports are leading up to the highly anticipated report on May’s employment situation from the Labor Department, including the unemployment rate, on Friday morning. Investors are mulling every piece of economic data trying to divine the next move of the Federal Reserve regarding its massive $85-billion-per-month monetary easing policy that has been attributed for the rise of the markets. The fear is that if QE3 is tapered, the markets could head towards bearish trends.

As a portion of its decision-making process, the Fed has said that they will not pull back on easing efforts until the unemployment rate drops significantly. However, other Fed officials, such as Esther George (president of the Kansas City Fed Bank) and Richard Fisher (president of the Dallas Fed bank) have been advocating reduction in the asset-buying program due to potentially detrimental long-term effects.