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A series of Co/Pt multilayers with perpendicular magnetic anisotropy has been grown by magnetron sputtering and characterized using magneto-optical Kerr effect measurements with a view to optimizing samples for current-driven domain motion applications. The influence of the thickness of both Co and Pt layers on the coercivity and switching behavior has been systematically investigated. The coercivity was found to depend strongly on the thickness of the Co layer and clear perpendicular magnetic anisotropy was observed in multilayer stacks with Co thickness ranging from 3 to 7 A. Upon increasing the Co thickness further the magnetization reverts to the in-plane direction and both the coercivity and the remanence drop rapidly, with the former becoming dominated by shape anisotropy. Increasing the thickness of the Pt buffer layer leads to improved perpendicular magnetic anisotropy with higher coercive fields. In contrast, the thickness of the Pt capping layers does not appear to have any systematic influence on the anisotropy in the range of 22-62 A. The coercivity can be further affected by the number of repeat Co layers in the stack due to exchange and magnetic coupling between adjacent Co layers. Upon increasing the thickness of the intermediate Pt spacer layer beyond 27 A, a transition from a coherent single-unit-like reversal to a sequential layer-by-layer reversal was observed. Structures with sharp switching fields and medium coercivity (50-150 Oe) have Co thickness fractions in the range 5 7 of the total stack height and should be well optimized for studying current-driven domain motion at low current densities.