Pay increases for American workers have continued to fall from highs reached during the post-pandemic reopening.

And that's as true for folks keeping the same job as it is for those finding a new gig.

According to new data from ADP released Wednesday, annual wage increases for workers who stayed in their same job increased at the slowest rate in nearly three years in June. For job changers, annual wage increases slid for a third straight month.

"We are in a different regime than we've been in the past where that job-stayer growth was either flat or even rising," ADP chief economist Nela Richardson said during a call with reporters on Wednesday.

"The question before us is just how low is [it] going to get? The idea that job stayer growth would go back to pre-pandemic levels is still being challenged."

In June, wages for job stayers rose 4.9% from the prior year, slower than the 5% pace seen in the prior month and the slowest growth since August 2021. Wages for workers who changed jobs increased 7.7% year over year, down from 7.8% the month prior and well below the 16.4% seen at its peak in June 2022.

Read more: How does the labor market affect inflation?

Richardson noted that the still-elevated pay gains for job switchers reflect there is still some tightness in the labor market amid other signs of slowing, a trend among a slew of recent labor market data.

New data from the Bureau of Labor Statistics released Tuesday, for instance, showed there were 8.14 million jobs open at the end of May, an increase from the 7.92 million job openings in April.

Overall, labor market data has largely shown continued signs of moving off the boil but not entering a rapid cooldown. Richardson reasoned a similar trend is playing out in ADP's data. The ADP Research Institute's National Employment Report showed 150,000 jobs were added to the private sector in June, a deceleration from the 157,00 job additions in May.

Richardson noted that a range of about 120,000 to 150,000 monthly job additions keeps the labor market in a sweet spot, where it's not flashing warning signs about a slowdown in the US economy but not overheating the economy, either.

And to Richardson, the real concern would be a sudden decrease in job gains.

"It's the rate in which the economy evolves, not necessarily the level," Richardson said.

"And if we see the cooldown go from gradual to steep, I think that's a warning bell."

With the unemployment rate at its highest level in more than two years and continuing unemployment benefit claims rising each week, economists remain wary of the labor market's trajectory.

On Wednesday, data from the Department of Labor showed nearly 1.86 million continuing unemployment claims were filed in the week ending June 29, up from 1.83 million the week prior.

"While layoffs for now remain low, we think the rise in claims reflects more workers applying for benefits because they are finding it more difficult to find jobs as the pace of hiring has slowed," Oxford Economics lead US economist Nancy Vanden Houten wrote in a note to clients on Wednesday. "Despite the recent increase, initial claims remain below the level we think would signal a significant slowdown in job growth."

Vanden Houten added, "Current labor market conditions allow the Federal Reserve to be patient before lowering interest rates, although recent favorable inflation data provide them latitude to respond to any unexpected weakening in the labor market."

Friday will bring the next major labor market update with the closely followed nonfarm payroll report from the Bureau of Labor Statistics.

The report is expected to show that 190,000 nonfarm payroll jobs were added to the US economy in June, with unemployment holding steady at 4%, according to data from Bloomberg.

Josh Schafer is a reporter for Yahoo Finance. Follow him on X @_joshschafer.

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