Given their high theoretical specific energy, lithium-oxygen batteries have received enormous attention as possible alternatives to current state-of-the-art rechargeable Li-ion batteries. However, the maximum discharge capacity in non-aqueous lithium-oxygen batteries is limited to a small fraction of its theoretical value due to the build-up of insulating lithium peroxide (Li₂O₂), the battery's primary discharge product. The discharge capacity can be increased if Li₂O₂ forms as large toroidal particles rather than as a thin conformal layer. Here, we show that trace amounts of electrolyte additives, such as H₂O, enhance the formation of Li₂O₂ toroids and result in significant improvements in capacity. Our experimental observations and a growth model show that the solvating properties of the additives prompt a solution-based mechanism that is responsible for the growth of Li₂O₂ toroids. We present a general formalism describing an additive's tendency to trigger the solution process, providing a rational design route for electrolytes that afford larger lithium-oxygen battery capacities.