We got my little girls earrings pierced when she was a baby and have had those same earrings till now (she is 2).  Eventually, she lost the back to one of those earrings so I bought these to replace.  They are great.  You screw on the stopper to the post and it has seemed to stay put.  Also, the stopper (or whatever the back part of the earring is called) is designed in such a way that it covers the post so it won't poke them when they sleep.