The product ? of the tether-to-satellite mass ratio and the probability of tether cuts by small debris must be small to make electrodynamic bare tethers a competitive and useful de-orbiting technology. In the case of a circular orbit and assuming a model for the debris population, the product ? can be written as a function that just depends on the initial orbit parameters (altitude and inclination) and the tether geometry. This formula, which does not contain the time explicitly and ignores the details of the tether dynamics during the de-orbiting, is used to find design rules for the tape dimensions and the orbit parameter ranges where tethers dominate other de-orbiting technologies like rockets, electrical propulsion, and sails.