Diversity has its checklist: gender, race, religion and, increasingly, sexual preference.

But what about weirdos?

You read that right: Weirdos. Misfits, flakes, freaks, screwballs—call them what you like. You know—and they probably know—who they are.

In our research at the Darden School of Business on how organizations can leverage difference to generate stronger performance, we’ve begun interviewing people whose colleagues flag them as, well, “different.”

Our initial findings suggest that these people often struggle as a result of their so-called “weirdness.” I hear stories of pain and of not fitting into a social world. Some of these people have stifled their offbeat creativity out of social fear, camouflaging their true selves because they think it’s not appropriate at work to be as they really are. They leave essential parts of themselves at the office door.

But that doesn’t necessarily mean that weird people settle for being unhappy. We’ve found some have been able to turn that struggle into positive energy and productivity. How? Some organizations have figured out how to support weird people so they can create value. They’ve discovered there is potency and innovativeness in certain kinds of weirdness that can help businesses thrive.

One company hired an executive who was difficult to work with: bright, innovative and very combative in his personal style. This company had a collegial and easygoing culture, and he clearly did not fit. Still, he had a long tenure with the company because he was “constructively disruptive,” persistently challenging the group-think and conflict-avoidance that had, in the past, stymied decision making.

Finding constructively weird people starts with knowing the strengths and weaknesses of your team and your company. Then it requires searching for the person with the attributes you need in order to compensate for what you don’t do well.

We’ve found weirdness manifests itself in two ways. One involves people who act weird just to oppose the norm. I call that the “little w” in weird. Little w is all about “me.” It makes you feel good to be different, but you’re not contributing to what is really needed. These weird people often have voracious egos.

In contrast, “big W” weird people also oppose the norm, but do so because they are trying to see something or to achieve a larger goal, and they know that following a normal path won’t get them there. Often these folks are more humble than their “little w” brethren, because they are just focused on getting a great result.

There’s much more to learn about the weirdness factor, but it’s becoming clear through our research that society needs to expand its definition of diversity to include the weird, because they can be the ones who will help an organization thrive.

Martin Davidson is a professor of business administration at the Darden School of Business. His website is leveragingdifference.com. A version of this article first appeared in BusinessWeek.