An asymptotic analysis of electron collection at high bias ⌽ p serves to determine the domain of validity of the orbital-motion-limited ͑OML͒ regime of cylindrical Langmuir probes, which is basic for the workings of conductive bare tethers. The radius of a wire collecting OML current in an unmagnetized plasma at rest cannot exceed a value, R max , which is found to exhibit a minimum as a function of ⌽ p ; at ⌽ p values of interest, R max is already increasing and is larger than the electron Debye length De . The breakdown of the regime relates to conditions far from the probe, at electron energies comparable to the ion thermal energy, kT i ; R max is found to increase with T i . It is also found that ͑1͒ the maximum width of a thin tape, if used instead of a wire, is 4R max ; ͑2͒ the electron thermal gyroradius must be larger than both R and De for magnetic effects to be negligible; and ͑3͒ conditions applying to the tether case are such that trapped-orbit effects are negligible.