FORTUNE — Let’s say you’re considering two candidates for a job. They have similar credentials and experience, but their personalities are poles apart. One is quiet, seems anxious, and lets you do most of the talking in interviews, apparently out of fear of saying something wrong. The other is talkative, engaging, and bursting with confidence. Which one do you choose?  Most hiring managers would opt for the second, extroverted candidate. Yet, for a job requiring teamwork, the anxious one, who shows signs of the personality type called “neurotic,” might be the better choice in the long run.  “It’s counterintuitive,” notes Corinne Bendersky, who teaches management at the Anderson School at UCLA. She is co-author of a study called “The Downfall of Extroverts and the Rise of Neurotics: The Dynamic Process of Status Allocation in Task Groups,” set for publication in the next issue of The Academy of Management Journal.  MORE: How IDEO brings design to corporate America  “Our research shows that extroverts are held in high esteem by their teammates at first, but over time, their performance tends to be disappointing,” Bendersky says. “By contrast, neurotics exceed everyone’s expectations and end up being highly effective team members.”  Why? “It’s mainly because neurotics try harder to please. The same anxiety that coworkers initially view as possibly disruptive is what causes neurotics to try extra hard to get along with others and perform well,” Bendersky explains. “Extroverts, on the other hand, are often poor listeners, impatient with others’ ideas, and not good collaborators.” So, over time, they contribute less than their teammates expected and lose status among their peers.  Bendersky and her research team discovered this by doing two experiments. In one of them, first-year MBA students took personality tests before being divided up into study groups of five people each. After the students had worked together for a week, everyone was asked to complete a survey evaluating their teammates, with emphasis on which members of each group had the highest status and were expected to perform the best.  The extroverts won that popularity contest hands down. “But when we repeated the survey after the teams had been working together intensively in five different classes for 10 weeks, we got a very different result,” Bendersky says. “The students whose personalities were more neurotic had exceeded expectations and gained status where extroverts had lost it.” The study “really showed a huge gap between expectations and experience.”  MORE: How to control workplace cruelty  That’s not to say you should fire all your extroverts. “They’re very good in some roles, especially client-facing roles like sales, for example,” Bendersky says. “But in jobs that require a lot of collaboration, they are often not as effective.  “We’ve probably overpopulated our teams with extroverts, because they do so well in job interviews,” she adds. “But the best teams have a mix of personality types.” If you’re leading a team that just isn’t performing as well as you’d hoped, Bendersky suggests, “try adding more neurotics to it” — if you’ve hired any.
They shine in job interviews, but outgoing, confident people often don’t perform well in teams, says a new study. Surprisingly, neurotics do.