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High precision measurements for back-angle quasi-elastic scattering of {sup 16}O from various target nuclei have been made, and are compared with coupled channels calculations to determine the diffuseness of the real part of the Woods-Saxon nuclear potential. The extracted diffuseness parameters are in the range of 0.60 to 0.69 fm, and agree well with previous results using a {sup 32}S projectile. The measured quasi-elastic energy spectra close to the barrier show both discrete peaks and a broad continuous structure with Q-values down to -25 MeV. These suggest the inadequacy of coupled channels calculations that include couplings only to low energy, discrete states of the colliding nuclei.