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The effect of strain on the magnetic anisotropy of epitaxial Co/Ni/Cu/Si(00l) structures was studied using polar magneto-optic Kerr effect WOKE) magnetometry and reflection high energy electron diffraction (RHEED). CO has the effect of reducing the perpendicular magnetic anisotropy of Ni for the whole range of Ni thicknesses (30 Å to 120 Å) while a variation of the perpendieular CO anisotropy constants with the Ni thickness is observed. The first and second order magnetoelastic coupling coefficients of CO were obtained from this strain-related variation, and are found to have opposite signs. We show that by varying the Ni thickness it is possible to sensitively control the magnetic anisotropy of the CO layer.