Maybe the market should start betting even more heavily on pushing that interest-rate hike toward July.

That's the message from Thursday's report on May private-sector hiring from payroll processor ADP (ADP - Get Report) , which shows hiring moderated for a second straight month. The nation's employers added 173,000 new jobs, up from a revised 166,000 in April.

Companies are, if not tapping the brakes on hiring, at least letting up on the gas as full employment approaches, said Mark Zandi, chief economist at Moody's Analytics, which prepares the report each month for ADP.

"The number was a solid number. The job growth is fairly broad-based, with a couple of sectors shedding payrolls, including the energy sector and manufacturing," Zandi said. ADP data "shows a definitive movement in wage growth."

The details: Manufacturing lost 3,000 jobs, as construction companies added 13,000. Services companies added 175,000, led by 43,000 new positions in professional and business services, 28,000 in the trade/utilities/transportation sector, and 13,000 in financial companies like Bank of America (BAC - Get Report) and JPMorgan Chase (JPM - Get Report) . Large companies added 34,000 jobs, small businesses 76,000 and medium-sized firms added 63,000.

The numbers almost exactly match expectations for 175,000 new jobs, as reported in a survey of economists by Econoday.

"Our forecast all along has been for a gentle deceleration in job growth over the course of this year, and I think that's what we're seeing," Regions Financial chief economist Richard Moody said. "This rate of job growth is more than sufficient to keep downward pressure on the unemployment rate."

The numbers do not suggest that tomorrow's unemployment report from the Labor Department will be strong enough to pressure the Federal Reserve to raise short-term interest rates at its June meeting, even though several members of the Fed's Open Market Committee have said a June hike is possible, Zandi said. The central bank is still likely to wait for the results of the June 23 vote in Britain on whether the United Kingdom should leave the Eurozone.

"If [tomorrow's report] came in at 160, the number consistent with today's ADP [data], and it showed continued employment in wage growth, that would all be consistent wth the idea that the Fed would raise rates, if not at the June meeting, then next month,'' Zandi said. "It''s not one of those numbers that says, 'I have to move now or I'll have a bigger problem down the road.' My sense is they'll wait til July. It would take a pretty strong report to get them off the dime and move it to June."

The figures are good news for the broader economy, both here and abroad, Zandi said. He argued that higher wages and nearly-full employment for U.S. workers will translate into more growth in consumer spending, which would support companies from McDonalds (MCD - Get Report) to Home Depot (HD - Get Report) . It would also be good for overseas companies that export to the U.S., he added.

ADP did not subtract the 35,000 workers at Verizon Communications (VZ - Get Report) who were on strike for part of last month from its employment estimate, Zandi said. The government's report is likely to subtract about 25,000 from its estimated job growth for the strike, he said. The Labor Department survey attempts to count how many workers were actually at work each month, so excludes striking workers. ADP counted them because they remained on Verizon's official payroll, Zandi said.

The rate of hiring is likely to slow in coming months as the economy approaches full employment, and may go as low as 100,000 new jobs a month, about half the average pace of the past five years, as firms have more trouble finding new workers, Zandi said. As that happens, growth in wages shuld accelerate, he added.

"It feels to me like the job market is very healthy," Zandi said."It's hard to identify any signifcant blemish. There's a fundamental reason for optimism about the U.S. economy, and it supports the global economy.''

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.