Do you breastfeed your baby to sleep? Lots and lots of mums do. Newborn babies seem to do little more than feed and sleep. Sometimes they only feed a short time and they are fast asleep, other times they are sleeping and feeding at the same time. In those early days breastfeeding and sleeping are closely linked and, because babies are so tiny, it is accepted that this is what happens. But as babies start to grow parents start to doubt whether this is the right thing to do.