"The statistics are pretty significant when talking about death," said Brown, author of "Baby 411: Clear Answers and Smart Advice for Babies in the First Year."
"Our parents put us on our bellies and, you bet, we did sleep better -- but at what cost?" she asked.
"The cost for sleeping on their backs is that there are kids who are going to have positional plagiocephaly," Brown told ABCNews.com. "But it's not life-threatening. Which would you choose? And the flat head's not for life."
Brown's patients have seen their flat heads normalized before they enter kindergarten.
"As a pediatrician, I'd rather have a kid with a flat head," Brown said. "We can work with the ear infections."