Future pulsed-power electronic systems based on dielectric capacitors require the use of environment-friendly materials with high energy-storage performance that can operate efficiently and reliably in harsh environments. Here, a study of multilayer structures, combining paraelectric-like Ba0.6Sr0.4TiO3 (BST) with relaxor-ferroelectric BaZr0.4Ti0.6O3 (BZT) layers on SrTiO3-buffered Si substrates, with the goal to optimize the high energy-storage performance is presented. The energy-storage properties of various stackings are investigated and an extremely large maximum recoverable energy storage density of ≈165.6Jcm-3 (energy efficiency≈93%) is achieved for unipolar charging-discharging of a 25-nm-BZT/20-nm-BST/910-nm-BZT/20-nm-BST/25-nm-BZT multilayer structure, due to the extremely large breakdown field of 7.5MVcm-1 and the lack of polarization saturation at high fields in this device. Strong indications are found that the breakdown field of the devices is determined by the outer layers of the multilayer stack and can be increased by improving the quality of these layers. Authors are also able to deduce design optimization rules for this material combination, which can be to a large extend justify by structural analysis. These rules are expected also to be useful for optimizing other multilayer systems and are therefore very relevant for further increasing the energy storage density of capacitors.