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Dedicated hierarchical structuring of functional ceramics can be used to shift the limits of functionality. This work presents the manufacturing of highly open porous, hierarchically structured barium titanate ceramics with 3-3 connectivity via direct ink writing of capillary suspension-type inks. The pore size of the printed struts (∼1 μm) is combined with a printed mesostructure (∼100 μm). The self-organized particle network, driven by strong capillary forces in the ternary solid/fluid/fluid ink, results in a high strut porosity, and the distinct flow properties of the ink allow for printing high strut size to pore size ratios, resulting in total porosities >60%. These unique and highly porous additive manufactured log-pile structures with closed bottom and top layers enable tailored dielectric and electromechanical coupling, resulting in an energy harvesting figure of merit FOM 33 more than four times higher than any documented data for barium titanate. This clearly demonstrates that combining additive manufacturing of capillary suspensions in combination with appropriate sintering allows for creation of complex architected 3D structures with unprecedented properties. This opens up opportunities in a broad variety of applications, including electromechanical energy harvesting, electrode materials for batteries or fuel cells, thermoelectrics, or bone tissue engineering with piezoelectrically stimulated cell growth.