A poll this summer of 1,215 U.S. managers and employees across a variety of industries, by EY (formerly Ernst & Young), found that members of Gen Y, aged 18 to 32, rank flexibility among the perks they want most, with 33% saying they wouldn’t work anywhere that didn’t offer it. But it seems Gen X values flextime even more: 38% of people aged 33 to 48 consider it non-negotiable, with men who said so, at 40%, slightly outnumbering women (37%).

“Companies first started offering flexible schedules, in the late ‘80s and the ‘90s, as a way to recruit and retain talented women, but it’s gone way beyond that now,” observes Karyn Twaronite, an Ernst & Young LLP partner who came up through the tax side of the business and now holds the title EY Americas Inclusiveness Officer.

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Noting that both men and women, in all age groups, ranked flextime tops among non-cash perks, Twaronite adds, “That result mirrors exactly what we’re seeing here at EY.” The accounting and consulting giant, No. 57 on Fortune’s Best Companies to Work For, has had thousands of employees working flexible schedules for years — including, since 2004, six weeks’ of paid leave for new dads.

“One myth is that men won’t take paternity leave,” says Twaronite. “In fact, I was in the meeting where we decided to start offering it, and there was a lot of skepticism there about whether men would take it.” Fast-forward nine years, and Twaronite says “90% of men here, including senior managers, do take at least two weeks, or they spread it out, taking two weeks now and up to four weeks later. The number of men and women taking parental leave now is exactly equal.”

Dan Black, EY’s Americas director of recruiting, says flexible schedules are “a major advantage in attracting talent, at the entry level right up through the ranks of experienced professionals.” He notes that Millennials’ insistence on not being bound by a 9-to-5 workday “has emboldened older people to talk about the need for flexibility. It’s a big factor in many candidates’ decision to come to work here.

“Flextime may have started out as a ‘women’s issue,’ but it’s morphed into something that people of both sexes have come to expect,” he adds. “I think it’s partly because of the large number of two-career households now, where people are having to accommodate two demanding professional schedules instead of just one.”

Black, whose wife is an attorney, speaks from experience: He has been working flexible hours since he joined EY 20 years ago and took four weeks of paternity leave for each of his two children. He now coaches his son’s soccer team, plays an active role at a couple of nonprofits, and serves as a volunteer firefighter in his hometown of Archville, N.Y.

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The EY survey suggests that, in the next decade or so, the opportunity for a life outside the office will become an even bigger draw — or deal-breaker — than it already is. Most of those polled still work a set schedule, the report notes, but “respondents anticipate a shift in the coming years to more flexible hours, as 62% currently work standard office hours and only 50% expect to do so in five to 10 years.”

That doesn’t surprise Karyn Twaronite. “Work is changing,” she observes. “The technology to connect anywhere, anytime, means that people are expected to be on call 24 hours a day, especially in global companies that operate across different time zones. The flip side of that is that employers are becoming more accommodating of people’s lives outside of work — because they have to be.”