the problem with thumbsucking

so we have been trying to get noe to stop sucking her thumb for almost a month now with varying degrees of success. she usually only did it to go to sleep or when she was really upset about something. at first, most nights and some naps she would go without the treasured philange pacifier. so she was rewarded for it. but then she started doing it as soon as she woke up. i'd catch her doing it while she watched a movie or played with a doll. sometimes she does it just to be funny. so we started threatening to wrap her hand up or take away privileges. so she started doing it at night again. so here we are, mixing rewards and punishments and showing no real sign of improvement. so this morning, she came downstairs to report that she hadn't sucked her thumb all night. this i knew to be a lie since she had it in her mouth when i checked on her at 1:30am and because her thumb was wet again when she came to me. so i gasped and looked down at her thumb really close and pointed to a half ring of chapped skin at the base of her thumb and said, "oh, my goodness, honey! look at your thumb!" of course, she did so with a three year old's version of worry...curiosity. i said, "do you see this? your thumb is breaking!" now i had her attention, so i continued. "you really have to stop sucking your thumb, noe, or it's going to break off!" she came back with, "you'll have to buy me another one?" so after explaining as simply as possible that she couldn't have another thumb (after all, daddy isn't made of money), i thought that i had properly scared her enough to keep her from committing the much complained about habit the rest of the day at least. if all else fails, scare the little buggers, right? well, it didn't work quite as well as i'd hoped. she was back at it for nap time (during which she did not take a nap, by the way). i have fears now, though, that she's going to wake up screaming tonight about a runaway thumb.