Some women are trying to push back against an unwritten set of responsibilities and expectations they say weigh them down at the office. Calls for so-called office housework – everything from booking meeting rooms to buying and circulating birthday cards to keeping team interactions friction-free – are interrupting the actual work they were hired to do.

“You know, I’m trying to help run a company,” says Claire Borger, 43 years old, who produces television commercials, podcasts and events for a living but often found herself tidying the office and tracking staff birthdays at a previous job. An attempt to pass the birthday calendar off backfired when the new person forgot to set it to repeat annually and colleagues peppered Ms. Borger with demands of, “How did my birthday get forgotten?” and, “Why didn’t you handle this?”

Managers are more likely to call on women for less glamorous tasks, researchers and workplace experts say, and women sometimes find themselves volunteering – feeling pressure to play the role of the chipper worker bee. While some employees of both sexes are trying to subvert stubborn gender dynamics, dodging office drudgery is complicated.

“I think to myself, ‘How would a male version of me behave?’ ” Jillian Vorce says of her frequent interactions with businessmen. Ms. Vorce is the 41-year-old founder of Jillian Group, a Boston-based strategic consulting firm. “I can’t be too controversial because they shut down. I can’t be too flimsy either because then they don’t respect it.”

A couple of years ago, she was helping a client pitch potential investors when one meeting attendee casually instructed her to take notes. Everyone besides her in the room, at a country club in Connecticut, was male.

“I stopped for a second. I looked at him. And I said, ‘Are your hands broken?’ ” Ms. Vorce recalls. He laughed, grabbed his legal pad and started to write.

“They never asked me to take notes from that point,” she says. “They just understood.”

Women can get dinged for resisting gendered roles and risk being labeled as difficult, says Joan C. Williams, director of the Centre for WorkLife Law at the University of California Hastings College of the Law. Meanwhile, men are asked less often to perform menial tasks and don’t face consequences when they decline.

“Women can totally thrive and survive in high-stakes, high-status workplaces, but only if they’re about twice as politically savvy as men,” Ms. Williams says. “If a man is presented with the office housework, here’s the strategy: say no. If a woman is presented with office housework, you try to do it once, do it gracefully and then work behind the scenes to try to change the system” – for example, moving from informal, ad hoc assignments to a set rotation.

In a 2016 survey of 3,093 engineers, Ms. Williams and colleagues found that 55% of women said they do more office housework than their peers of both genders, while 26% of white men said they carry more of the load. She says the unequal distribution of office housework is a key reason women leave companies.

Emotional labor, like having to soothe workplace tensions, also often falls to women. Alexa Crisa, a 30-year-old digital marketer in Atlanta, says she was once asked to go on a business trip that had little to do with her own job. Her presence was requested so she could be the peacemaker between two feuding colleagues, she says.

“It was just stressful,” Ms. Crisa says. “You’re thinking, ‘This isn’t what I should have to worry about when I come to work every day.’ ”

Regular days at the office have their little challenges as well, says Ms. Crisa, who seldom uses exclamation marks for fear of being perceived as cold if she were to skip them later, and pushes colleagues to help her plan parties so she’s not the only one doing it. In an environment that often feels fraught for women, Ms. Crisa says she values male allies who do small but concrete things, like publicly emphasise if an idea was hers.

Asked what it takes to be “a good guy” in the office, Ms. Crisa responds with a message for the men: “I don’t need you to feel sorry for me,” she says. “Just be a good friend.”

Interviews with other women turned up stories of male colleagues who fit the bill: the man in Texas who routinely brought in coffee for his team at a tutoring centre; or the male boss in Illinois who informed a female worker that her new male colleague was hired for more money—and who got her a pay bump to equalise their salaries.

When told how much their efforts mean, the office’s good guys generally respond with a confused shrug.

“It’s my management style,” says David Haray, a health-care consultant in Columbus, Ohio, who takes notes in meetings and often praises his male and female staff’s work to higher-ups.

“It takes barely 30 seconds to change the Bounty,” says David Or, a director of product engineering at New York-based Arkadium, which makes games for online publishers and advertisers. He replaces the paper towels in the company kitchen, dumps water out of the dispenser tray and cleans up after monthly board-game nights. “I don’t consider them chores,” he says.

If men could use a pep talk about ramping up office housework, the one for women would go like this: sit down.

“Did you leave that there? Don’t pick it up,” Jessica Rovello, Arkadium’s CEO, says she told women she noticed cleaning up glasses that male employees left in the company’s conference rooms after meetings.

Other female leaders preach about literally sitting on their hands, for example when coffee orders are ready to be passed out to meeting attendees.

“Don’t be afraid of silence,” Carmel Galvin, the chief human-resources officer at software maker Autodesk, counsels women who find themselves constantly volunteering to take notes. “Count to five, wait for the pause.”

Some women are heeding the call. Enrica McDaniel, who works in human resources for an insurance company in Plano, Texas, avoids offering to do things like plan parties for fear of being considered less strategic or serious as a black businesswoman. Besides, she has noticed that few others at the companies she’s worked for seem to care about things like whether she decorated a colleague’s office for his birthday.

“We may look at that as an entryway, ‘Oh I’m volunteering, I’m being a team player,’ ” she says. “But, overall, there’s no value to that.”

Anna Dapelo-Garcia, a 57-year-old executive with Palo Alto, Calif.-based Stanford Health Care, spent years dutifully taking notes and projecting a sunny demeanour to colleagues before realising it wasn’t going to win her a promotion.

“It didn’t matter how nice I would be. I’d be the note taker, the coffee maker,” she says.

She grew up watching the Latina women in her family cook and clean and brought that servant mentality to the office, she says, until during a performance review in her early 40s, her male boss urged her to speak up more in meetings.

“I thought, ‘Holy crap. Whoa,’ ” she says. “What was that about? Being the greeter, being the smiley face. I don’t have to do any of those things.”

– Ms. Feintzeig is a Wall Street Journal reporter in New York. Email her at [email protected].