We report two methods to create zinc-sponge electrodes that suppress dendrite formation and shape change for rechargeable zinc batteries. Both methods are characterized by creating a paste made of zinc particles, organic porogen, and viscosity-enhancing agent that is heated under an inert gas and then air. During heating under the inert gas, the zinc particles anneal together, and the porogen decomposes; under air, the zinc fuses and residual organic burns out, yielding an open-cell metal foam or sponge. We tune the mechanical and electrochemical properties of the zinc sponges by varying zinc-to-porogen mass ratio, heating time under inert gas and air, and size and shape of the zinc and porogen particles. An advantage of the reported methods is their ability to finely tune zinc-sponge architecture. The selected size and shape of the zinc and porogen particles influence the morphology of the pore structure. A limitation is that resulting sponges have disordered pore structures that result in low mechanical strength at low volume fractions of zinc (<30%). Applications for these zinc-sponge electrodes include batteries for grid-storage, personal electronics, electric vehicles, and electric aviation. Users can expect zinc-sponge electrodes to cycle up to 40% depth of discharge at technologically relevant rates and areal capacities without the formation of separator-piercing dendrites.