For the third week in a row, and for only the sixth time since the Great Recession officially ended in June 2009, new weekly filings for jobless benefits are under the 400,000 mark on a seasonally adjusted basis, the Labor Department reports. Last week, initial claims slipped by 6,000 to 388,000. The four-week moving average of claims remains well under 400k as well, continuing a trend that’s been in place for over a month.

“The modest pace of layoffs is allowing job gains to accelerate,” Joel Naroff, president of Naroff Economic Advisors, told Bloomberg before today’s report was released. “Businesses are hiring. And with layoffs being minimal, it appears that the labor market is indeed getting better.”

The improvement, however, remains slow and therefore vulnerable to the proverbial unknown unknowns. Although the trend in new claims is favorable in terms of direction, the cycle remains lethargic. Consider the much larger population of existing claims, which tracks unemployed workers who have been collecting jobless benefits for some time. Although the tally here has been falling steadily for nearly two years, the recent 3.714 million total is still well above even the cyclical peaks of the last two recessions.

All of which implies what’s well understood in the market: the labor market is likely to continue recovering, but surprises in favor of growth will be minimal. Economists are expecting that tomorrow’s nonfarm payrolls report for March will report a net gain of just under 200,000, or roughly in line with February’s rise. A respectable gain, but far short of spectacular, and therefore far short of what’s needed to make a material dent in February’s 8.9% unemployment rate–the highest level since 1983.