The error introduced into a tethered-balloon measurement of the atmospheric potential by the plume of space charge drifting downwind from the conducting tether is analyzed. A number of simplifying assumptions yield a mathematically tractable model capable of placing an upper bound on the relative magnitude of this error in terms of the height achieved by the balloon. Relaxing the most severe of these assumptions allows more realistic error estimates at the expense of some loss of rigor. It is concluded than an altitude of between one and two conductivity scale heights is sufficient to reduce the error below 10%.