The Labor Department is proposing to expand overtime eligibility to include most salaried workers earning less than about $35,000 a year.

The new threshold would be substantially higher than the current level of about $23,700, but would cover fewer workers than an Obama administration initiative that was thrown out by a federal judge.

Under the proposal announced today, most workers earning less than the new threshold must receive time-and-a-half pay when they work more than 40 hours a week.

The department anticipates that the rule will expand overtime eligibility by just over 1 million workers, assuming their employers don’t adjust their salaries or work schedules in response.

The proposal will be subject to a 60-day public comment period, and the department expects it to take effect around January. The current threshold was set by the George W. Bush administration in 2004.

The Obama administration set the salary threshold at about $47,500 when it put forward a new rule in 2016. But a federal judge in Texas suspended the rule just before it was to take effect, arguing that the administration lacked the authority for such a significant increase. The same judge later invalidated the Obama rule.

While the Trump administration has appealed the judge’s decision, it asked the court to pause the appeal while it prepared a new version of the rule.

Heidi Shierholz, a former Labor Department chief economist who was involved in the Obama administration’s effort, said that the threshold in the new proposal was at the upper end of what she had expected, but that she was still disappointed with the figure.

“Their analysis of the rule looks similar to what we did,” said Shierholz, now director of policy at the liberal Economic Policy Institute. “The problem is their own analysis shows millions fewer workers get covered.”

But Tammy McCutchen, one of the architects of the Bush administration’s increase, said she was pleased that the department had set the threshold at about the 20th percentile of earnings for salaried workers in the South — in line with where she and her colleagues had set it in 2004.

“I think that’s what they had to do in light of the Texas court decision,” said McCutchen, a lawyer at the management-side firm Littler Mendelson. “Anything higher would have been subject to challenge again.”

Many employers and business groups argued that while the 2004 threshold was in need of an increase, the magnitude of the Obama change was unreasonable.

Some argued that it would significantly increase costs for employers, who would either have to pay out hundreds of millions more in overtime or raise workers’ salaries above the new threshold to avoid paying additional overtime. Many critics also said salaried workers would suffer a loss of status by having to account for their time the way hourly workers do.

The Obama administration argued that its proposal was modest by historical standards, noting that it would make fewer than 40 percent of salaried workers eligible for overtime pay based on their salaries, far less than the percentage who were eligible in 1975.

Even so, it estimated that more than 4 million workers would gain the right to overtime pay under its rule.

Other skeptics argued that the change would have little impact because employers would lower the base wage of people who work significant overtime hours, leaving their total pay, including wages and overtime, roughly unchanged.

More liberal economists largely rejected this analysis and concluded that while base wages might fall somewhat, the increased overtime pay would more than offset the losses.

Employees who make more than the salary threshold are also eligible for overtime pay if they aren’t executives, administrators or professionals — that is, workers who have significant decision-making authority. But the Obama administration believed that employers were routinely flouting this so-called duties test by labeling rank-and-file employees as managers, making a high salary threshold more important.

The Trump administration’s original nominee for labor secretary, fast-food executive Andrew Puzder, was openly hostile to the Obama overtime rule. But after he withdrew his nomination because of a personal controversy, his replacement, Alexander Acosta, struck more of a middle ground.

At his confirmation hearings in 2017, Acosta suggested that a reasonable salary threshold would be in the low $30,000s.

Last year, Acosta’s department held a series of public “listening sessions” to solicit input from employers, business groups and worker advocates on where to set the threshold. Many in the business community echoed his $30,000-plus suggestion, while worker groups tended to favor the Obama threshold.

“At my confirmation hearings, I committed to an update of the 2004 overtime threshold, and today’s proposal would bring common sense, consistency and higher wages to working Americans,” Acosta said in a statement.

In addition to raising the salary threshold, the Obama administration’s approach also required that it rise automatically every three years to keep up with salary increases. The new proposal does not seek to raise the threshold automatically, but suggests that it be updated through a new rule-making process every four years.