While it's true that one should take the slack out of cables, that doesn't have anything to do with the noises he's trying to fix.
It's one or more of the "rear end" things others have suggested (worn cogs, derailleur alignment, b-tension adjustment, or simply not trimming the derailleur fully).
How much effort the OP wants to put into smoothing out this noise depends on how much it's driving him nuts, I guess.