The giant magnetoriesistance (GMR) effects in sandwiched Co/Cu/Co and Co/CuMn/Co structures have been investigated. The GMR oscillates with the spacer thickness for both cases, but nearly antiphased. With diluted Mn atoms in the Cu spacer, the GMR curve as a function of the magnetic field changes a lot, and the saturation/switching field for GMR can be reduced greatly compared with that in Co/Cu/Co systems. This may suggest one way to obtain a highly sensitive GMR.