My baby hasn't arrived yet, but I fully expect the hats to be too big for some time after birth.  I mostly purchased this set for the mittens as my first born gouged herself immediately with her tiny, sharp little nails.  Ever clip or file a day old baby's nails?  Not fun.  Very cute set though.  Be careful not to stretch out the elastic in the mittens, I would fold them on themselves like you would socks... but quickly discovered this would stretch out the elastic and cause them to constantly fall off baby's hands.