Babies suck their thumbs as a way of self soothing, a natural way to settle themselves to sleep. mine both suck their thumbs, my 6yr still does it but only to go to sleep at night, i know he will stop eventually. i stopped at 7 and my brother at 5. my 4mth old daughter does it and she is very happy, settles herself to sleep, sleeps all night and has done from 10 weeks. i do occassionally hear her wake a little, suck her thumb and go back to sleep without crying. i did use dummies a little on both of them for a few weeks around 6 weeks, as they do need to suck at this age and some find it hard to keep thumb in, but as they learnt around 10 weeks i got rid of dummies. i am not sure why you want to stop your 3yr old sucking his thumb? he will probably stop himself in a couple of years and i'm not sure its possible to make him stop. i dont think bribery will work and if you give it lots of attention he might do it even more! of course its up to you if you wan tto use a dummy but I am not that keen on dummies myself, mainly because of what you say about them falling out all the time, also because its the parent who decides when they have it and that is often when they dont need it, my daughter does not have her thumb in her mouth all the time, but i do see lots of children with a dummy in all the time. its not that nice to see older children out with a dummy in and i do see that a lot. if the reason you asked this question was to get more sleep at night then the thing to remember, if you are not already doing is to help your baby to settle themselves to sleep, not to feed or rock to sleep and for them to wake up in same place they fell asleep. you could try singing or rubbing tummy to help them settle. 3 mths is still quite young but i would stop night feeds around 3-4 mths and just offer water or try to settle them. As they get older they will wake just because you feed them and give comfort, not because they need a feed.