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Both of my girls were really attached to their binky. Like breaking any habit, it was difficult to take it away, but I learned a great tip in the process.
First, gather all the binkies in the house, so your child can't find one. Then take one binky and cut the very tip of it off with a pair of scissors. Every day thereafter cut a little more off.
This worked wonders with my girls. It was no longer: "Mommy is taking this away from me!" It became instead: "What the heck is wrong with my binky?" I remember one of my girls calling it the "yucky binky." Whenever she wanted a binky, this is what she got and she decided it wasn't what she wanted anymore. There were some tears, but it was nothing personal.
Note: I did this just days following their first birthdays, but this could work at any age.

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