In the design of materials for the shielding of electric devices, there is a recent trend to use multilayer compounds due to some restrictions in the making process of the materials but also since they are supposed to have a higher potential to offer “better” characteristics than the related monolayered materials. In this work, we investigate the possible impact of the number of layers in a compound critically. It will turn out that—at least for the general objectives we study here and for conducting polymer composites—multilayered materials are suitable to only a limited extent. To be more precise, when “just” aiming for a high shielding efficiency the task can be accomplished with merely one layer. If in addition the cost of the material comes into play, however, a second layer may be helpful, but further layers do not seem to have a significant impact on the performance of a material. Here we extend an existing multiobjective design problem for the design of shielding materials for our purpose, and attack the resulting multiobjective optimization problem with evolutionary strategies, and finally analyze the results in the viewpoint of the required number of layers within a shielding material.