The national hospital chain

HCA Healthcare Inc.,

HCA -0.69%

which struggled to find enough nurses and other workers throughout the pandemic, says hiring is up and turnover is down. At

Uber Technologies Inc.,

UBER -0.50%

more people are signing up to work as drivers or food couriers.

Marriott International Inc.,

MAR 0.80%

meanwhile, says it is seeing steady improvement in its hiring, with wage increases slowing, too.

Corporate leaders say the job market still favors workers over employers and that challenges remain in drawing enough staff. Still, many say the worst of the hurdles appear to be over.

“We are not running around with our hair on fire, if you will, anymore,”

Bill Hornbuckle,

chief executive of casino operator

MGM Resorts International,

told investors Wednesday, though he added that it is hard to hire for certain positions such as housekeepers and cooks.

The economy has now made up the number of jobs lost in the aftermath of the pandemic, and demand for workers is fierce. In July, employers added 528,000 jobs, far more than expected, and the unemployment rate fell to a half-century low of 3.5%. There are indications that workers are also accepting jobs more quickly, economists say, reducing some of the burdens for companies looking to fill positions.

Companies cite varying factors in explaining hiring successes.

Kroger Co.

told investors in June that some employees who left to work elsewhere had returned to the grocery chain.

Uber,

UBER -0.50%

which struggled with too few drivers to meet demand over the past year, said inflationary pressures motivated more people to drive for the service.

Uber

ended its latest quarter with a record number of drivers, CEO

Dara Khosrowshahi

said last week.

“For the people who are looking for work right now, they’re very willing to take it, and that’s why you’re seeing high levels of payroll growth,” said

Nick Bunker,

an economist at job-search platform Indeed.

Fears of a recession or inflation also appear to be keeping some workers in their existing jobs, economists and executives say, leading to a drop in turnover in some industries—another boost for companies. The rates of quitting in both hospitality and retail have fallen in recent months from peaks earlier in the pandemic, Mr. Bunker said, though they remain elevated historically.

“We had this very large churn that was creating this bottleneck in jobs, and that bottleneck is being eased out,” said Bledi Taska, chief economist at Lightcast, a labor-market analytics company.

On earnings calls in recent weeks, many CEOs said that turnover ticked down. Attrition at government contractor

Booz Allen Hamilton Holding Corp.

has returned to pre-Covid levels, CEO

Horacio Rozanski

said in late July. At HCA, the hospital operator, turnover fell more than 20% in the second quarter compared with the first, CEO

Samuel Hazen

said. Employee retention also rose at

Bloomin’ Brands Inc.,

parent of restaurant chains Outback Steakhouse and Bonefish Grill.

“We are seeing the staffing environment improve,” Bloomin’ CEO

David Deno

told analysts in late July. “We’re seeing that in our metrics and our labor metrics, be it retention, be it staffing, be it turnover.”

Some companies say they have had more success hiring recently as pandemic-related challenges, such as the closure of trade schools, eased. Last summer, the manufacturing company

Graham Corp.

, which employs about 500 people, found it so difficult to hire welders for a facility in upstate New York that the company resorted to bringing on contract workers at elevated pay rates. “We were in a really bad spot,” CEO

Dan Thoren

said.

The situation is now being reversed, in part because trade and vocational schools have reopened and begun graduating welders again, he said. Graham is working to hire some of those new to the field from such schools. But it is also receiving more applications from experienced welders, too, something it largely didn’t experience even a few months ago. Mr. Thoren attributes the applications to the company’s efforts to create a desirable workplace, but also to a changing economy and job market where workers may seek greater stability.

“It is still a very tight market, but we are seeing some softening,” Mr. Thoren said. “I think people are saying, ‘OK, we’ve had a chance to try out greener pastures and we’ve done that and now we’re going to start to settle.’ ”

Some prominent employers, including

Walmart Inc.,

Oracle Corp.

and

Robinhood Markets Inc.,

have laid off workers recently, while tech giants such as

Facebook

owner

Meta Platforms Inc.

have slowed hiring. Yet many more companies are hesitant to cut staff, economists and executives say, after doing so at the start of the Covid-19 pandemic and then finding it difficult to quickly rehire workers as needed.

While some bosses feel confident in their abilities to hire now, many also remain concerned about a shortage of workers.

International Business Machines Corp.

has more than four million people in a database of applicants, CEO

Arvind Krishna

said in a recent interview as part of a Wall Street Journal CEO Council event. “That makes us feel good that we can get enough right now,” Mr. Krishna said, before adding, “That’s an area where we’re paranoid: There’s so much competition for tech skills.”

Employers hiring for a range of roles, from hourly retail jobs to advanced technical positions, say they are noticing a change in job seeker sentiment and behavior.

Samantha Hammock,

chief human-resources officer at

Verizon Communications Inc.,

said it is taking less time to fill open roles in software engineering, front-line sales and retail and other positions because fewer applicants now have multiple offers at the same time.

During earlier periods in the pandemic,

Verizon

often found that it would extend an offer to a candidate, only to be told that the worker was weighing three other job offers. If the candidate declined

Verizon’s

job, its recruiters would need to start the process over to find someone else, Ms. Hammock said. “That really does extend the time to fill” a job, she noted.

Now, as

Verizon

makes offers, candidates are more likely to accept them, she said, part of what she described as a softening in the labor market. In finding workers, “It is still hard, but it’s improving,” she said.

Write to Chip Cutter at chip.cutter@wsj.com