It was recently suggested that the magnetic field created by the current of a bare tether strongly reduces its own electron-collection capability when a magnetic separatrix disconnecting ambient magnetized plasma from tether extends beyond its electric sheath. It is here shown that current reduction by the self-field depends on the ratio L*/Lt parameterizing bias and current profiles along the tether (Lt ≡ tether length, L* ≡ characteristic length gauging ohmic effects) and on a new dimensionless number Ks involving ambient and tether parameters. Current reduction is weaker the lower Ks and L*/Lt, which depend critically on the type of cross section: Ks varies as R5/3, h2/3R, and h2/3 ¿ 1/4 width for wires, round tethers conductive only in a thin layer, and thin tapes, respectively; L* varies as R2/3 for wires and as h2/3 for tapes and round tethers conductive in a layer (R ≡ radius, h ≡ thickness). Self-field effects are fully negligible for the last two types of cross sections whatever the mode of operation. In practical efficient tether systems having L*/Lt low, maximum current reduction in case of wires is again negligible for power generation; for deorbiting, reduction is <1% for a 10 km tether and ~15% for a 20 km tether. In the reboost mode there are no effects for Ks below some threshold; moderate effects may occur in practical but heavy reboost-wire systems that need no dedicated solar power.