Electroaerodynamic (EAD) thrusters have the potential to become a quieter and solid-state alternative to propellers in unmanned aircraft. An EAD thruster produces ions from atmospheric air and accelerates them across an electric field between two electrodes: an emitter, where ions are produced; and a collector, where they are neutralized. As ions drift from the emitter to the collector, they collide with neutral air molecules and transfer momentum to them, resulting in an ionic wind and a thrust force. Reverse emission from the collector is a major non-ideal effect in EAD systems that can reduce the efficiency of EAD thrusters: it increases the power draw of the device and eventually leads to electrical breakdown and sparking. Here, we perform a parametric study with a wire-to-cylinder electrode geometry using positive and negative corona discharges as well as wire-to-wire dielectric barrier discharges as ion sources. We show that reverse ion emission is primarily caused by a gas discharge at the tips of the cylindrical collectors, which increases current without contributing to thrust and produces audible noise. We identify three ways to mitigate reverse emission: increasing the collector diameter, increasing the collector span with respect to the emitter span, and attaching hemispherical end caps to the collector. By mitigating reverse emission, we show that the power draw of an EAD thruster can be significantly reduced (by up to 64% in our particular configuration) while still delivering the same thrust.