A pulsed‐current technique was used to measure the extendedI–Vcharacteristics of a wide variety of prototype high‐temperature‐superconductor (HTS) leads. It was found that the average resistivity rises withJ(≳Jc) more gradually than in conventional superconductors—often remaining very small compared to silver, for values ofJ(≫Jc) that are high enough to be practically useful. This observation, combined with the low thermal conductivity (∼50 times smaller than Ag), should extend the utility of HTS leads to the dissipative regime whereJ/Jc≫1. ©1995 American Institute of Physics.