Weird brake!!!

2005 Cavalier. Right rear brake works fine with a gentle,touch. But, with a heavy foot, a few feet before total stop, there is a clicking noise with a frequency of about one click per revolution. I replaced both rear drums, readjusted both rear brakes through the little window on the back side. The inside of the drum is smooth, both brake shoes are smooth. There is no pulling or grabbing, just this irritating click, click, click. Any thoughts???? Thanks, Joe