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This really works. I got my sister out of her Verizon contract last time they bumped up the rates. It was something like 75 cents more for one of those extra fees they tack on.
They said that it was so small, what did it matter? I said, "If it's such a small deal, why are you bothering to add it to my bill?" They offered to credit us the 75 cents per month back. I was insistent that it was a material change and we were tired of being nickled-and-dimed and we wanted out. I was nice about it, but firm. It worked.
So if you want to stick it to the man, now is the time to do it. Actually, the time to do it is 60 days within the time they send you notification. Better to do it sooner than later.
More details can be found here.