Unsafe bedding is the cause for a majority of unexpected deaths among infants, according to a new study from the Centers for Disease Control and Prevention. Soft bedding like pillows, blankets, crib bumpers and stuffed animals remain the leading cause for accidental suffocation among babies under four months of age and younger.

For decades, public health messages have centered around informing new parents of the dangers of preventable suffocation. Unfortunately, the latest research reveals that approximately 3,500 babies die annually due to sudden unexpected infant death, or SUID, in the U.S. SUID is the all-encompassing term for the sudden unexpected death of a baby under age 1. It includes SIDS, or sudden infant death syndrome, as well as accidental suffocation in sleep environments.

The study analyzed data from 4,929 cases of SUID from 2011-2017. In 72 percent of those deaths, soft bedding was the cause. Because young infants are unable to move suffocation hazards themselves or move away from them, hazards like soft bedding present an obstacle in their ability to breathe.

While co-sleeping with little ones is often a last-resort tactic for many sleep-deprived parents, it still poses serious risks to infants.

“We’re also talking about infants being placed on surfaces other than a bassinet or crib—a couch, a recliner or an adult bed,” said the study’s author, Sharyn Parks, senior epidemiologist at the CDC’s Division of Reproductive Health told NBC News. “We’re seeing babies who are dying in all of those circumstances.”

Just 1 percent of the deaths analyzed were confirmed as having been unexplained without any soft bedding or other unsafe sleep surfaces. Factors for the other 27 percent couldn’t be determined because of insufficient information.

According to the American Academy of Pediatrics (AAP), a SUID death might be from suffocation via airway blockage or tangled in bedding and blankets, infection, choking, injury, or a cardiac or metabolic dysfunction. When an infant death can’t be explained, the baby is determined to have died from Sudden Infant Death Syndrome (SIDS).

Thanks to the “Back to Sleep” campaign in the 1990s, SUID cases declined rapidly once parents began to put newborns to sleep on their backs rather than their stomachs. When the campaign began in 1994, nearly 4,700 babies had died of SUID the previous year. By 2010, the number of such deaths had been cut in half, according to the American Academy of Pediatrics.

Unfortunately, the number has not continued to decline since 2010. Public health experts believe messaging about safe sleep environments should happen when parents are still expecting, and should be encouraged to come up with a safe sleep plan ahead of their baby’s birth.

“These deaths are still happening–and they happen to well-meaning parents,” Dr. Rachel Moon, who chairs the AAP task force on SIDS and authored the AAP policy statement on safe infant sleep, told CNN. “Bed-sharing rarely occurs in the absence of pillows and blankets,” Moon said.

The AAP recommends, if possible, caregivers should keep the baby’s crib in their bedroom for at least six months, preferably until the baby is one year old. Though the “back is best” public health messaging on sleep position is very important, caregivers can’t forget about the risks of unsafe bedding. Babies should always be placed on their back for sleeping, but the AAP states they also need a firm, flat surface inside a crib or bassinet (or other separate, similar surface) with a tight-fitting sheet only.

“I know that it is hard to do safe sleep for each and every sleep, but please keep doing it!” Moon added. “Remember that the safest baby is one who is on the back, in a crib or bassinet or another flat, firm surface, without anything in it.”

Being able to rest when you’re a new parent surely doesn’t come easy, but you’ll be able to breathe a sigh of relief by practicing safe sleep habits with your little one from day one.