The magnetocaloric response of Ni-Cu based multilayers has been studied with the aim of optimizing their magnetic field dependence. In contrast to the behavior of single phase materials, whose peak magnetic entropy change follows a power law with exponents close to 0.75, multilayering leads to exponents of -1 for an extended temperature span close to the transition temperature. This demonstrates that nanostructuring can be a good strategy to enhance the magnetic field responsiveness of magnetocaloric materials.