Either-or. Both my children love the dummy. Now that my son is two, I'd like for him to give the dummy up sooner rather than later, mainly for the sake of his teeth. I just remember when the "dummy fairy" took my dummies away though, and I don't want there to be an evil fairy involved. (I started to suck my thumb as soon as my dummy was gone anyway). I got a great piece of advice from a couple of women from mothers group the other day, who said, let him chew a hole in it and decide to give it up for himself (cutting off any loose bits), instead of buying new ones. I think that's a great gradual way to go about it, and it should be gradual enough that he wont be tempted by his thumb.