Solid-oxide fuel cells produce electric current from energy released by a spontaneous electrochemical reaction. The efficiency of these devices depends crucially on the microstructure of their electrodes and in particular on the three-phase boundary (TPB) length, along which the energy-producing reaction occurs. We present a systematic maximization of the TPB length as a function of four readily controllable microstructural parameters, for any given mean hydraulic radius, which is a conventional measure of the permeability to gas flow. We identify the maximizing parameters and show that the TPB length can be increased by a factor of over 300% compared to current common practices. We support this result by calculating the TPB of several numerically simulated structures. We also compare four models for a single intergranular contact in the sintered electrode and show that the model commonly used in the literature is oversimplified and unphysical. We then propose two alternatives.