Mr. Mabry said that in some parts of the country, workers would walk off the job knowing that they could find another restaurant hiring down the street. Still, he said, Mooyah can’t just raise pay across the board — the burger industry is “a pennies business,” Mr. Mabry said, and wage increases quickly eat into profits.

Instead, Mr. Mabry said, he is looking for ways to make restaurants more efficient by reducing turnover, improving morale and cross-training workers for various jobs. The goal, he said, is to be able to pay higher wages to fewer workers.

Mooyah is also trying to recruit untapped sources of talent. The company recently started a program to help franchisees expand their marketing efforts by hiring at-home parents and others who had not been in the labor force. The jobs are meant to appeal to people who might not be looking for traditional work: They do not require being at an office every day or having a traditional schedule. Mr. Mabry said that kind of flexibility made sense when filling full-time slots with experienced workers was harder than ever.

“Why do I have to be pigeonholed into a particular résumé or a particular experience?” Mr. Mabry said of his recruitment approach. “I’m sure there is someone out there who can bring something different to the team. It’s just having an open mind.”

More companies are likely to adopt that kind of flexible approach as the labor market tightens. And there are other signs that companies are rethinking their approach to hiring. They are becoming more willing to consider candidates with criminal records, for example, or to waive educational requirements. The car retailer AutoNation said this week that it was no longer refusing to hire workers who tested positive for marijuana use — a sign of changing legal and societal norms, but also an indication that companies are rethinking hiring practices in a tight labor market.

“People who are marginally employable suddenly become highly employable in a period like this,” said Joseph Brusuelas, chief economist of RSM, a financial consulting firm.

There were some notes of caution in Friday’s report. The total number of hours worked — a measure that combines the number of jobs and the average hours worked on those jobs — fell slightly, a sign that demand for labor might not be as strong as the headline job-growth figures suggest. And the unemployment rate for African-Americans, a figure highlighted by Mr. Trump after it fell to its lowest recorded level in December, jumped nearly a full percentage point, to 7.7 percent. The unemployment rate for white Americans fell to 3.5 percent.