To cope, companies are doing more for existing employees to convince them to stay and becoming less picky in choosing new ones to come on board, said Paul McDonald, a senior executive director at Robert Half International Inc., a Menlo Park, California-based staffing firm.

And they’re raising wages. Robert Half projects that salaries for professionals in such fields as accounting, finance and specialized administration will rise 4.1 percent this year after increasing 3.8 percent in 2015.

Gimbel though said that workers remain restrained in pushing for higher pay packets. "Everybody has gotten a little bit wiser after the Great Recession," he said.

Wage data reported by the government have yet to show much, if any, drift upwards. Average hourly earnings of private-sector employees rose 2.3 percent in March from a year earlier, in line with increases seen throughout the expansion.

Carl Riccadona, chief U.S. economist for Bloomberg Intelligence, said that’s a sign that there’s still slack left in the labor market. He said the market has "decent momentum" though he adds that the strong picture painted by payrolls has been tarnished by other indicators showing less vibrancy.

Funk, for his part, is wary. "We’re watching it real closely," he said.

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