They are old enough to bargain with, I am going to have to deal with this when my daughter is older, she loves her binky, mostly when she is tired though. See if they can use it at night, if they want it in the day, offer sugar free lollypops. When they ask for them say they are for bedtime, and say if they wait they can have a lillipop, or something they love. We both are at an advantage, a binky you can take away, a thumb you cannot. My husband is a dentist, and although binkies are not the best thing for oral devolopment, it is better than a thumb. I say bargain away, kids are super smart, but switch the candies (use sugar free as often as possible)so they dont expect a strawberry jolly rancher each time. For each day they go without binkies, they get to put a sticker by their name. Amounts of stickers add to prizes, geting to eat dessert first, getting a dollar for each 5 stickers, you know where I am going. Stickers work wonders... the points system can be used to get them motivated to potty, clean the room... it gives them something for their work. Let me know how it goes.