Last week, I wrote about how powerfully protective whooping cough vaccines can be when babies receive their first dose before even being born, from their pregnant mothers-to-be. As I was looking through that study, another of its findings struck me: Babies didn’t seem to get any extra whooping cough protection when their moms were vaccinated after giving birth.

I wondered if this meant that I was unreasonable when I insisted my parents be fully boosted before visiting their first granddaughter. If post-birth vaccinations aren’t that important for mothers, who are entwined in every way imaginable with their newborns, is it likely that grandparents’ vaccination status is all that important?

The practice of making sure people who come into contact with a vulnerable newborn are up on their shots is called “cocooning.” The idea is based on straight-ahead logic: By eliminating dangerous germs from those people, the newborn is protected. She can’t catch what isn’t there.

While it’s a good idea to make sure everyone is current on vaccines, the evidence for cocooning as a way to keep infants healthy has been lacking. “I haven’t seen any studies that show a strong protective effect form the cocooning strategy,” says Nicola Klein, the pediatrician and vaccine researcher who led the recent Pediatrics study on vaccinations for whooping cough.

Some of the evidence that questions the cocooning strategy comes from a study of Australian babies. In 2009, cases of whooping cough began to increase in Western Australia. In 2011 and 2012, health officials there offered free vaccines to new parents, grandparents and others who had close contact with newborns. It was a good idea, but it didn’t seem to work, researchers reported in 2015 in Vaccine. Whooping cough rates were similar between babies whose parents had been vaccinated in the 28 days after their children were born and babies whose parents were not vaccinated.

That’s just one study, and it has its limitations. The researchers couldn’t trace the route of infections in these infants; infections could have come from older siblings or even people who were vaccinated but still carried the germs. And the data were gathered from birth and vaccination records, which may not have been perfect. But overall, the study didn’t reveal big benefits for babies whose families practiced the cocooning strategy.

Even if post-birth vaccinations don’t protect babies that well, vaccinating parents, grandparents and other people who snuggle babies is “certainly not a harmful thing or a bad thing,” Klein points out. Anything that may curb the spread of whooping cough is actually a very, very good thing, both for the person getting vaccinated and all of us in the herd.

Still, it seems that the cocoon strategy pales in comparison to the protection offered by vaccination during pregnancy, an approach that the Centers for Disease Control and Prevention recommends. When mothers get vaccinated during pregnancy, protective antibodies zip through the placenta straight into the baby. “It’s not just the indirect effect of protecting the mom, so it’s therefore protecting the baby,” says Klein, of the Kaiser Permanente Vaccine Study Center in Oakland, Calif. “This is actually directly giving an immune response to the baby when you vaccinate during pregnancy.”