WASHINGTON — Carmel Bender started her new job the day her mother had brain surgery, and quickly used all the paid time off for which she was eligible.

Bender couldn’t afford to quit, “but I didn’t want to be sitting at my computer while my mother died,” she said.

Thanks to a popular benefits program that let co-workers donate unused leave to Bender, she was at her mother’s bedside when needed. And when she wasn’t, Bender, 51, was at her desk at the Washington office of the giant accounting firm KPMG LLP, never missing a paycheck.

Systems for donating leave are surging among companies, which see gains in worker loyalty through greater flexibility in dealing with their outside needs. Last year, nearly a third of U.S. employers permitted leave donations, based on a survey of 320 companies by CCH, a business information and service provider based in Riverwoods, Ill. That’s up from 20 percent in 2004 and 23 percent in 2005.

Among big employers with leave-donation programs are American Airlines, Marriott Corp., Kaiser Permanente, UnitedHealth Group, Charles Schwab and every U.S. government agency.

“We’re seeing tremendous interest in this area,” said Carol Sladek, a principal at Hewitt Associates in Lincolnshire, Ill., a leading human resources consulting firm. “Everyone’s looking for ways to help employees balance work and life.”

Hurricane Katrina spurred many of the programs, according to M. Michael Markowich, a Philadelphia-based personnel consultant. Workers at national companies pressed their employers for new ways to help co-workers in New Orleans and the Gulf Coast region, he said.

Instigation by workers is typical, according to Connie Rank-Smith, the vice president for human resources at Jewelers Mutual Insurance Co. in Neenah, Wis. Its 175 employees have been donating leave to one another for a decade.

“Someone is off caring for a very ill child or a parent, and our people want to know what they can do to help,” Rank-Smith said. “Well, they can take over a casserole, but they can do more than that. They can donate a day of their own paid time. And people feel very good about doing that.”

According to Kevin McFadden, a senior KPMG audit manager who donated time to Bender, “It doesn’t really matter whether you know who the person is or not. You get great satisfaction from knowing you’re helping someone in need and it’s a co-worker.”

Hospitals and nursing homes, which have complex scheduling problems, high turnover and large female work forces, got into donated leave early, consultants said. So did employers with traditions of generous benefits, including colleges and universities, and local, state and federal governments. The federal program, which started in 1987, helps thousands of workers yearly.

“It’s also a good recruitment and retention tool,” said Jerry Mikowicz, the pay and leave director at the federal Office of Personnel Management. “People appreciate that if something comes along and they need help, their fellow employees will be there to take care of them.”

The main downside, said Sladek, who’s designed about a dozen leave-donation plans, is dealing with hard feelings among time-seekers when donors are tapped out or unmoved by a particular case.

Well-designed programs cost employers nothing or save a little money, Sladek continued. That’s because donated-leave programs usually stipulate that only time is given — not hourly wages — and the pay grades of donors tend to be higher than the pay grades of beneficiaries.

Federal workers can donate leave time that they’d otherwise forfeit at year’s end, but private-sector deals generally are stricter. Typically, they require workers to donate vacation time rather than unused annual sick leave.

Donation schemes are easiest to devise at companies that have eliminated separate accounts for vacation, personal and sick leave. They create a single simple category — paid time off — whose use workers control.

Standard rules prohibit workers seeking help from campaigning for it and keep donors and beneficiaries anonymous. The donor gets no tax deduction. The recipient pays the same taxes that would be due if there’d been no interruption.

Most donation accounts fill up fast, KPMG and others report, and pay an extraordinary dividend: time when it’s precious.

For Bender and her mother, Isabelle Williams, who died Nov. 13, 2005, it was time to “sit beside her and talk to her even though she couldn’t respond except to squeeze my hand,” Bender said.

“I’m very, very grateful,” she said. “Even though KPMG is very large, I feel that we’re a family — that we have human relationships rather than co-worker encounters.”