In early May, a group of about 20 Twitter employees gathered at the company's New York offices to swap stories about becoming new parents. They shared strategies for prepping to go out on leave for nearly three months. They lamented their loss of sleep. They traded ideas for limiting e-mail intrusions after the baby arrives and cutting back on travel once they head back to work. (Pro tip: Take the red-eye flight to be home for bedtime.)

These weren't working mothers. They were men attending the social media company's second "Dads on Leave" roundtable. Twitter offers 10-week paid paternity leave.

"It was enormously valuable and reassuring to know that this leave isn't just a front," said Jason Toff, the general manager for Twitter's Vine business. He plans to split his time off in two, taking five weeks when his first child is born in July and the other five later this year, likely around the holidays. "They explicitly encouraged us to take the leave and [said] don't worry."

Such corporate nudging is rare — which often makes taking advantage of paternity leave still something of a leap of faith. "In most settings there's still a stigma," said Stewart Friedman, a Wharton professor. "You're penalized in subtle ways if you take time away."

Recent research has shown that men who request family leave are less likely to be recommended for pay raises or promotions.

That may change, however, as more companies promote the policies they have or even introduce more generous ones. Richard Branson announced last week that a small subsection of his employees at Virgin — those working for his company's investment and brand licensing arm, Virgin Management — would have access to a year of paid paternity.

In May, Johnson & Johnson announced that fathers would get nine weeks of paid parental leave, up from one. And just this month, Goldman Sachs doubled its paid leave for "non-primary caregivers" to four weeks.

For some employers, this reflects an effort to be more inclusive for same-sex couples or adoptive parents. For others, it may be a reaction to some of the research linking paternity leave, and male spouses' involvement at home, to benefits for women's careers. Yet, perhaps most commonly, it's a move to compete for talented young male employees who want more flexibility and greater involvement in their children's lives.

"Men and women are much more alike now in what they think it takes for a dual career to work," Friedman said. "There's much more exploration into alternate ways of living. The zeitgeist has clearly shifted."

Fatherly, a Web site featuring stories about things like iPad apps for children and a dad raising his kids at sea, lists its 50-best companies for dads; it highlights Twitter (No. 11), as well as Google (No. 1), Bank of America (No. 3) and Patagonia (No. 4).

"The scenario we are in today is a far cry from the father works, the mother does not," said Simon Issacs, a Fatherly co-founder. "Progressive companies are changing their practices."

At Google, for instance, employees who are equal or primary caregivers can get 12 weeks of paid "baby bonding time," regardless of gender. At Bank of America, all new parents can get 12 weeks paid. At Patagonia, fathers get eight weeks paid.

But plenty of companies are not so progressive. Data from the Bureau of Labor Statistics show that only 13 percent of U.S. full-time employees had access to paid family leave in 2012 — and it seems likely that much of that was maternity leave.

Even among the most generous companies for new parents, the average length of paid leave for fathers is only about three weeks, according to Working Mother Magazine's editorial director Jennifer Owens.

And then there's still the question of whether male employees feel comfortable taking it. When PricewaterhouseCoopers made changes to its policies last year, it not only effectively expanded the number of weeks available for many dads, it also renamed its program — partly in hope that more fathers would take advantage of the benefit. Instead of referring to "primary" and "non-primary" caregivers, it now simply uses the phrase "parental leave."

While the old policy was intended to be gender-neutral, said Jennifer Allyn, managing director of diversity at PwC, the firm realized people don't necessarily identify themselves that way. "There's a barrier with the gender norms around who considers themselves the primary caregiver," she said. "We didn't want to have distinctions between mothers and fathers."

That switch to discussing "parental leave," rather than separate maternity and paternity benefits, is a move more companies have been making recently, said Carol Sladek, who leads work-life consulting at Aon Hewitt.

"The idea is to be more about work and life," she said, "instead of saying here's a benefit for this group and here's one for that group."

Others are finding ways to bring more visibility to the men who have taken paternity leave, especially those in leadership roles.

Research has shown that when men see other men take leave, it has an impact. A study from last year found that men in Norway were more likely to use paternity benefits if they had a brother or co-worker who had.

That's another reason Toff, at Twitter, is planning to take all the leave he's been offered. He has 10 direct reports, and a total team size of 40 — all but one of whom don't yet have children. He said he hopes to set an example. "Both for my own sake, but also for my team's sake," he said, "I'm going to use this policy and spend that time with my child."