Dear Annie: I was recently put in charge of a team of 13 people, with the goal of finding new ways to appeal to diverse consumer markets, including people ages 18 to 30 and different ethnic groups (all ages). Everyone on this “cross-functional” team was picked because they are stars in their various areas, so I know they each have a lot to contribute. The trouble is that, at every meeting we’ve had so far, a few very confident team members always seem to suck up all the oxygen in the room, while others rarely utter a peep. One is very young, so I think she’s intimidated by the more experienced people who do most of the talking. A couple of others, for whom English is a second language, are even quieter. Any suggestions about how to encourage them to speak up? — Listening in Los Angeles

Dear Listening: No doubt, plenty of other team leaders are wondering, too. Since roughly half the population is made up of introverts, who tend to mull things over carefully before they open their mouths, most teams include at least one or two members who don’t say much. “On diverse teams, when people come from cultures where offering ideas or opinions isn’t encouraged, the challenges are multiplied,” notes David Livermore, president of training and consulting firm Cultural Intelligence Center. In a new book, Driven by Difference: How Great Companies Fuel Innovation Through Diversity, Livermore offers some suggestions you might find helpful, based on the firm’s research and its work with clients like Procter & Gamble, IBM, Walmart, Bank of America, and Google.

First, you may have to redefine what you mean by “speaking up,” because the phrase may strike some of your team members as uncomfortably assertive. Team leaders “need to clarify what they want, which is usually not to have everyone talking all the time,” Livermore says. “Be sure to explain clearly, especially to a culturally diverse team, that your goal is to gather ideas from everyone. Remind them of it regularly.”

Then, try one of these ways of collecting team members’ thoughts:

Make it a homework assignment. Ask each person to write down his or her ideas on a given topic in advance. “Then ask them to bring their written thoughts to the meeting for a systematic discussion” where everyone at the table gets a turn, says Livermore. “This allows the less vocal members of the group to have their ideas considered alongside those of the people who’ve been quicker to speak.”

Gather everyone’s ideas, and write up a formal agenda. This approach takes a bit more effort on your part as the team leader, but it works. Ask everyone to send you his or her thoughts via email or text. Once you have each person’s contribution in hand, you can decide how to order the discussion, and send out a full agenda far enough ahead of time so that everyone has chance to think about everyone else’s ideas. Consider making all suggestions anonymous, so no one is swayed (pro or con) by whose idea it was.

Make a few phone calls before the group meets. You already know who “sucks up all the oxygen in the room,” as you put it, and who’s been trying to fade into the wallpaper. So Livermore recommends a brief, private chat with each of them. Thank the most vocal people for their enthusiasm, which you genuinely do appreciate (right?). But, since you’re concerned with making sure everyone’s ideas are heard, could they do you a favor at the next meeting and wait until you call on them before they speak? As for the quiet ones, let them know you’re looking forward to hearing what they think.

It’s no coincidence that each of these methods involves making your expectations clear before the whole team gets together. Says Livermore, “Not only does advance warning reduce the anxiety of participants who don’t like to be put on the spot, but all team members are likely to have better input if they spend some time thinking about it beforehand.”

That may be especially true for your team members whose first language isn’t English. “Even if someone is very fluent, the person might be mentally translating what’s being said into his or her native tongue, and then back into English again, before offering a comment,” Livermore observes. “It takes a little longer, which often means the discussion has moved on to a new topic before that person gets a chance to speak.”

This is one reason why, when it comes to gathering ideas from team members who bring with them very different personalities and backgrounds, meetings are overrated. If you haven’t already done so, encourage people to share their ideas with you one-on-one. “You can say something like, ‘I’d like to hear back from everyone by the end of this week. You can either offer your input at our meeting this afternoon, or talk with me afterwards, or send me an e-mail,’” writes Livermore in Driven by Difference. You might be pleasantly surprised at who suddenly has a lot to say.

Talkback: Have you ever belonged to a team that was dominated by one or two vocal members? How did you get your ideas heard? Leave a comment below.

Have a career question for Anne Fisher? Email askannie@fortune.com.