For as long as Brad Johnson can remember, he has never been able to sleep more than six hours a night. Most nights, he sleeps even less. Mr. Johnson, 63, always wakes without an alarm clock, feeling rested and ready for the day.

“If you paid me $100,000 to sleep eight hours tonight, I couldn’t do it,” he said.

He’s not the only one in his family like this. Two of his seven siblings also are natural short sleepers. He suspects that their father was one, too.

At least 15 years ago, he said, one of his brothers reached out to a sleep doctor at the University of Utah, who took an interest in the family, collecting blood samples and conducting interviews at a reunion. Ultimately, researchers identified six members of Mr. Johnson’s extended family, men and women, who get by on an average of less than six hours of sleep a night , much less than the eight and a half hours that people typically need to function at their best.

Researchers wondered whether there was something about their genetics that might help explain how sleep works for the rest of us.