Pediatricians have long urged parents to put newborns to sleep on their backs to help prevent sudden infant death syndrome. While the practice undoubtedly has saved lives, it also has increased the numbers of babies with flattened skulls.

Roughly 1 baby in 5 under the age of 6 months develops a skull deformation caused by lying in a supine position. Now a study has found that a common remedy for the problem, a pricey custom-made helmet worn by infants, in most cases produces no more improvement in skull shape than doing nothing at all.

The new report, published May 1 in the journal BMJ (formerly the British Medical Journal), is the first randomized trial of the helmets. The authors found “virtually no treatment effect,” said Brent R. Collett, an investigator at Seattle Children’s Research Institute and author of an accompanying editorial.

Skull flatness at back of the head may be accompanied by facial asymmetry: One ear may be slightly farther back than the other, and sometimes the side of the head can flatten. Until now, less-rigorous studies had mostly shown helmets did help normalize head shape.

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“I was very surprised at the results,” Dr. Mark R. Proctor, an associate professor of neurosurgery at Boston Children’s Hospital, said of the new study, adding that it was “rigorous.”

Still, the study leaves open the possibility that the helmets may be useful for infants with severe skull flattening and those with tight neck muscles, which make it hard for infants to turn their heads, so they remain in one position. Researchers from the University of Twente in the Netherlands assigned 42 babies who had misshapen skulls and were 5 to 6 months old, to wear a custom-designed helmet that allows flattened areas room to round out as the infant’s skull expands.

Parents were instructed to have infants wear the helmets 23 hours a day for six months or so. Another 42 babies with similar deformities received no treatment. Infants with the most severe deformities were excluded.

After two years, a researcher who did not know which babies had worn helmets evaluated skull shape in the infants. The improvements were not significantly different between the helmet-wearers and the infants not wearing helmets.

“There are definitely cases of infants with mild to moderate skull deformation who are treated with helmet therapy, and this study confirms and reaffirms that this is not necessary,” said Dr. James J. Laughlin, an author of the policy statement on skull deformities for the American Academy of Pediatrics.

Helmets to treat flattened skulls range from $1,300 to $3,000. Laughlin said the paper provides pediatricians and worried parents “reassurance that not doing helmet therapy will give you the same results as doing helmet therapy, which is expensive” and can be “stressful for the family.”

Makers of custom helmets questioned the study’s results. Tim Littlefield, a spokesman for Cranial Technologies, called it “inherently flawed.” William Gustavson, a spokesman for Orthomerica, called it “alarming” that nearly three-quarters of parents whose children received helmets in the study reported that the helmets shifted or rotated on their infants’ heads.

“The value of this research is fully reliant upon the quality of the fit,” said James Campbell, vice president of the American Orthotic and Prosthetic Association, a trade group.

Some surgeons worried that the finding would be applied too broadly, jeopardizing insurance coverage for severely affected children who could benefit from helmets.

“What I fear happening is that children with a severe deformity are going to be denied helmets based on this evidence, which is really only talking about moderate cases,” said Dr. Alex A. Kane, the director of pediatric and craniofacial surgery at UT Southwestern and Children’s Medical Center in Dallas.

Courtney Reissig, 31, a stay-at-home mother in Little Rock, Ark., doesn’t regret the eight months her son Luke wore a helmet. He had neck muscles so tight that he favored lying on his left side in bed, to the point that the side of his head “looked like the side of a toaster — flat, not round,” Reissig said.

He outgrew his first helmet, which cost $1,300, and required a second, she said. But wearing a helmet helped round out his head, and he now closely resembles his twin, Zach. “I do feel like the helmets were worth it,” she said.

Only about a quarter of the babies in the BMJ trial made a full recovery by the age 2.

“This is a problem we created,” said Proctor, of Boston Children’s Hospital. “All parents are told is sleep the child on their back. They aren’t told about flat heads and how to prevent it.”

Some pediatricians and specialists advise parents to try repositioning an infant’s head before considering a helmet. Repositioning entails alternating to which side the infant’s head turns once he or she is asleep on the back.