Recently, batteries with interpenetrating electrode architectures have been proposed which have the potential to outperform classical designs. These electrode structures are highly percolating particle distributions with short diffusion distances. One of the main advantages with respect to classic rocking chair battery designs is the decrease of the ohmic losses and localized joule-heating, while simultaneously delivering higher power densities and specific energies closer to the theoretical ideal. In the present paper, the rocking chair lithium-ion battery architecture is taken as a point of reference to explore two variations of a three-dimensional battery concept. The first microstructure possesses a highly branched tortuous positive electrode particle distribution, and the second architecture corresponds to a topology with perfectly ordered branches of positive electrode materials. Both architectures outperform the classic rocking chair design by a factor of five for intermediate discharge rates and by 37% for high discharge rates; however, branch ordering has the advantage of improving the macroscopic discharge time by 18% for discharge rates of 4C or higher. Simulations show that the power density of a rechargeable battery can be engineered by maximizing the electrochemical driving force for intercalation while decreasing the characteristic transport distances of the material components. Additionally, the analyzed devices greatly diminish the possibility of salt precipitation during discharge due to removal of microstructure limitations in the classic design. Results also show that for the interpenetrating architectures, when lithium plating and fracture fatigue do occur, they initiate at the tips of the branches of anode material, particularly in those regions that are closer to the electrode phase of opposite polarity. Increasing branch tortuosity induces lithium depletion at the back ohmic contact of the positive electrode at high discharge rates. (C) 2007 The Electrochemical Society.