NEW YORK (CNNfn) - Two steps forward, one step back -- that sums up the June employment report. A slow gradual turnaround in the labor market appears to be under way and there are straws in the wind suggesting it will continue. So far the glass is barely more than half full. But that's much better than being less than half-empty.

Let's start by looking at the net number of new jobs created outside the agricultural sector, aka non-farm payrolls. They rose just 36,000 in June, and both April and May were revised sharply lower; May's 41,000 increase was whittled down to 24,000, and April's 6,000 worker increase turned into a loss of 21,000. Only 39,000 jobs net new jobs were added to the U.S. economy in the second quarter. Not so hot.

One reason for the less-than-stellar growth in jobs in June was manufacturing, which lost another 23,000 jobs -- the 23rd straight month this sector has shed workers. However, that was less than half of the average loss of 52,000 manufacturing jobs in the previous six months. And it's a big improvement over the darkest recession months, from March 2001 to January 2002, when manufacturing lost 115,000 jobs a month on average.

The service sector accounts for about 80 percent of U.S. economic activity, including everything from department stores and restaurants to legal services and hospitals. In June, it added a net 46,000 workers. But in a healthy, growing economy, the service sector often adds three or four times that many workers each month, so this is hopeful but nothing to write home about -- yet.

A positive leading indicator here is temporary workers. Firms often hire temps when demand is picking up and they aren't ready to commit to the monthly benefit costs that accompany permanent hires. Temp workers grew by 9,000 in June, and even though it was far less than the 44,000 average increase of the three previous months, it was the fifth straight month this sector added employees, so it's a good sign.

One of the biggest pluses economists have pointed out is an increase in the workweek in June. That's important because it suggests that demand is picking up enough for employers to ask their employees to work longer hours -- even as many apparently are still too worried about the sustainability of that pick-up in demand to start hiring new workers.

"If you go back three-to-six months ago, payrolls were declining quite substantially and now it looks like payrolls have leveled off," said Robert Melman, economist at JP Morgan Chase, on CNNfn Friday. "The number of layoffs are still there, but not nearly as much. And I think firms are just sitting here.

"Business is coming in, housing's doing great, consumer spending is doing OK, manufacturing is picking up but they're just a bit cautious about hiring," Melman added. "Profit margins just got crushed in the last recession. they're worrying about their accounting and so forth and I think they'll be a little bit conservative about hiring from here."

And employers aren't the only ones who are cautious. The number of job-leavers as percent of total unemployed -- known as the "quit rate" -- hit a six-year low in June. Economists at Credit Suisse First Boston interpret this as showing that worker insecurity is back, that employees are staying put rather than testing the labor market waters.

But many economists remain convinced that caution will gradually give way to optimism and increased hiring in the months ahead. Brian Wesbury of Griffin Kubik Stephens and Thompson Inc. is definitely one who sees the latest numbers as more confirmation of a turnaround in the labor market and the economy, not a hint that a double-dip recession could lie ahead.

Like others, Wesbury points to the increase in the work week in June, another sign firms are seeing increased demand even if they are still too cautious to hire workers. And he also points to the recent decline in new claims for unemployment benefits back to the levels of March of last year when the recession just started.