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In this paper, we have measured damping in four sets of at least eight samples with either a normal metal (NM)/Permalloy (Py) or NM/Py/NM structure and varying layer thickness. These are, respectively Cu x/NiFe 50 nm/AlOx Ag 10 nm /NiFe x/Ag 10 nm, Cu 10 nm /NiFe x/Cu 10 nm, and Ta 5 nm /NiFe x/Ta 5 nm, where the layer with a thickness labeled x is the one that has been varied. We have measured the damping parameter from the ferromagnetic resonance (FMR) linewidth for all series and, after controlling for broadening phenomena, we have estimated the Gilbert parameter of each as a function of thickness. From these, we find that increasing the Permalloy layer thickness reduces the damping as 1/x, with the damping in the Ag and Cu multilayers decreasing at a third of the rate of the Ta multilayers, and we find that increasing the normal metal thickness increases the damping linearly from 0.01 at 100 nm to 0.11 at 2050 nm of copper-a vast and unprecedented change.