The ultra high-pressure U.S. job market may finally be starting to release a little steam.

• That's the key takeaway from new job numbers that show an extremely healthy labor market that nonetheless seems to be moving toward a less overheated state.

Driving the news: Employers added 390,000 jobs in May, the Labor Department said — the lowest job growth in a year. The unemployment rate was unchanged at 3.6%, holding close to the lowest levels seen in the past half century.

• Other details suggested a job market starting to come into balance. The number of adults in the labor force — either working or looking for work — rose by 330,000.
• Wage growth, while still strong at 0.3% for the month, receded from its recent highs. Over the last year, average hourly earnings are up 5.2%, compared to 5.5% in April.

State of play: Policymakers at the Federal Reserve and in the Biden administration want to see a labor market that is still healthy but cools from its red-hot levels seen earlier in the year, which tend to fuel higher inflation.

• "If average monthly job creation shifts in the next year from current levels of 500,000 to something closer to 150,000, it will be a sign that we are successfully moving into the next phase of recovery," President Biden wrote in a Wall Street Journal op-ed this week.
• "This kind of job growth is consistent with a low unemployment rate and a healthy economy."
• In that sense, the May numbers are what they hope to see — a gradual deceleration in the labor market, but not a sudden stop.

The bottom line: Policymakers are attempting a difficult, and potentially impossible, task in trying to cool off inflation pressures without a recession. But things went according to plan in May.

Editor's note: This story has been updated with new details.