For children who are premature, have reflux, live among smokers or are under four months old, "yes, it's risky on the stomach," said David. "It's less risky after six months, when babies are flipping themselves."
This flat head phenomenon comes as a surprise to many mothers.
"I don't remember the pediatrician telling me about it," said Stephanie Goldman, a special events manager for the New York office of the South African Ubuntu Education Fund. "The baby nurse told me, otherwise I wouldn't have known."
While back sleeping has cut SIDS deaths, it confounds mothers who say babies prefer their tummies.
Goldman swaddled her newborn in a Velcro wrap to help her adjust to her back.
"I'd put her to sleep like a little egg roll," Goldman told ABCNews.com. "Some people do it for a year."
She also has heeded advice to prevent flat head by repositioning her daughter with bolsters under crib sheets. Goldman and other mothers plan "tummy time" during the day to help strengthen neck muscles that tummy sleepers use in bed.
Pediatricians also recommend time spent outside the crib in car seats, carriers and activity gyms and that draw their heads to a new position. Pacifiers at bedtime, long demonized by doctors, are now recommended to prevent SIDS.
But all the fuss associated with back sleeping often surprises grandparents who raised their own children with the opposite advice.
"My mother-in-law said, 'What do you mean you put her to sleep on her back -- I've never heard of that.'" said Goldman.
But they agreed to disagree with the pediatrician who recommended waking a sleeping baby to eat.
"She was growing and eating and thriving," said Goldman.
"There definitely was a lot of conflicting advice when I first had the baby," said Goldman. "I stopped reading books, they were so overwhelming. One book said do this, and the other said do that -- feed on demand, feed on a schedule, swaddle or don't swaddle."
"What I realized after the anxiety attacks of the first week was, do what makes sense for you and your family," she said. "Trust your instincts as a parent."
Her friend Lindsay Sarnoff did just that.
"When my daughter was a newborn we were going crazy trying to get her to sleep," said Sarnoff, who worked for Ralph Lauren before having her second child this year.
"The first six weeks of her life, she slept on our chest on her tummy," she said. "But it got to the point where we couldn't sleep and it was dangerous if she rolled off."
But one afternoon in frustration, she placed her daughter on her stomach and the baby slept three hours.
"It was genius," Sarnoff said.
Her pediatrician agreed to the day plan, as long as Sarnoff was close by, but not at night. Soon, they put the baby in the bassinette in their bedroom one night with satisfying results.
Now, Sarnoff has a newborn son and "from day one" has put him down on his stomach.
"He's been sleeping well since he was eight days old," she said.
Though she is afraid to confess to her doctor, Sarnoff said she has the support of her own mother.
"My mom says, 'You guys slept on your stomach,'" she said.
But even with risks of head flattening, which in its most severe form can cause the ear to move forward, preventing fluid drainage, doctors are adamant about recommending back sleeping, even during nap time.
Dr. Ari Brown, a pediatrician from Austin, Texas, said the risk of SIDS far outweighs the risk of complications with a flat head.